Title: Apparatus and method for simultaneously displaying a number along with its number of significant figures
Abstract: A computing device (40) comprises an electrical circuit and a software application. A display screen (138) and an input device (140) are electrically coupled to the electrical circuit. The software application provides instructions to determine the number of significant figures for a number entered via the input device, and simultaneously display on the display screen the entered number along with the number of significant figures for the entered number, and/or the software application provides instructions to calculate a floating point answer for a mathematical operation entered for one or more numbers entered into the computing device, round the floating point answer to the proper precision or to the proper number of significant figures, determine the number of significant figures for the rounded answer, and simultaneously display on the display the rounded answer and its number of significant figures.
Patent Number: 6,854,001 Issued on 02/08/2005 to Good, et al.
| Inventors:
|
Good; John C. (Greenfield, NH);
Prestridge; Shawn (Plano, TX)
|
| Assignee:
|
Texas Instruments Incorporated (Dallas, TX)
|
| Appl. No.:
|
013992 |
| Filed:
|
December 11, 2001 |
| Current U.S. Class: |
708/174; 708/513 |
| Intern'l Class: |
G06F 003//14 |
| Field of Search: |
708/174,171,513
|
References Cited [Referenced By]
U.S. Patent Documents
| 4225932 | Sep., 1980 | Hirano et al. | 708/162.
|
| 4279022 | Jul., 1981 | Abe | 708/110.
|
| 4847802 | Jul., 1989 | Ashton | 708/513.
|
| 5289394 | Feb., 1994 | Lapeyre, deceased | 708/142.
|
| 5377130 | Dec., 1994 | Frank et al. | 708/142.
|
| 5768164 | Jun., 1998 | Hollon, Jr. | 708/174.
|
| 6044392 | Mar., 2000 | Anderson et al. | 708/551.
|
Primary Examiner: Malzahn; D. H.
Attorney, Agent or Firm: Moore; J. Dennis, Brady, III; W. James, Telecky, Jr.; Frederick J.
Claims
What is claimed is:
1. A computing device comprising:
an electrical circuit comprising:
a processor, and
a memory device electrically coupled to the processor;
a display screen electrically coupled to the electrical circuit;
an input device electrically coupled to the electrical circuit; and
a software application stored in the memory device, and when executed by
the processor, the software application being adapted to provide
instructions to:
determine the number of significant figures for a number entered via the
input device, and
simultaneously display on the display screen the entered number along with
the number of significant figures for the entered number.
2. The computing device of claim 1, wherein the computing device is a
calculator.
3. The computing device of claim 2, wherein the display screen comprises a
liquid crystal display device.
4. The computing device of claim 2, wherein the input device comprises a
keypad on the calculator.
5. The computing device of claim 1, wherein the computing device is a
handheld portable computing device.
6. The computing device of claim 5,
wherein the display screen comprises a touch sensitive screen, and
wherein the input device comprises a simulated keypad displayed on the
touch sensitive screen, such that a user can input a number or
mathematical operator by contacting the touch sensitive screen with a
touch wand.
7. The computing device of claim 1, wherein the computing device is a
laptop computer.
8. The computing device of claim 1, wherein the computing device is a
desktop computer.
9. The computing device of claim 1, wherein the computing device comprises
a server and a terminal, the computing device being structured in an
application service provider model such that the terminal is remotely
located from the server, the display screen and input device being parts
of the terminal, the electrical circuitry being part of the server, and
the display screen and input device being electrically coupled to the
electrical circuit via a network connection.
10. The computing device of claim 9, wherein the network connection
comprises the Internet.
11. The computing device of claim 9, wherein the network connection
comprises a local area network.
12. The computing device of claim 1, wherein the software application is
further adapted to provide instructions to determine the number of
significant figures for a second number entered via the input device, and
simultaneously display on the display screen the second entered number
along with the number of significant figures for the second entered
number.
13. The computing device of claim 12, wherein the software application is
further adapted to provide instructions to:
calculate a floating point answer for a mathematical operation entered,
wherein the entered numbers are the operands,
determine the proper number of significant figures for the floating point
answer based on the number of significant figures for each of the
operands,
round the floating point answer to the proper number of significant figures
for the answer, and
simultaneously display on the display screen the rounded answer along with
the number of significant figures for the rounded answer.
14. The computing device of claim 13, wherein the software application is
further adapted to provide instructions to simultaneously display the
floating point answer on the display screen along with the rounded answer
and the number of significant figures for the rounded answer.
15. The computing device of claim 12, wherein the software application is
further adapted to provide instructions to:
calculate a floating point answer for a mathematical operation entered,
wherein the entered numbers are the operands,
determine which of the operands is least precise,
round the floating point answer to least precision of the operands,
determine the number of significant figures for the rounded answer, and
simultaneously display on the display screen the rounded answer along with
the number of significant figures for the rounded answer.
16. The computing device of claim 1, wherein the memory device comprises a
flash memory device.
17. The computing device of claim 1, wherein the memory device comprises a
hard drive.
18. The computing device of claim 1, wherein the memory device comprise a
synchronous dynamic access memory (SDRAM) device.
19. A computing device comprising:
an electrical circuit comprising:
a processor, and
a memory device electrically coupled to the processor;
a display screen electrically coupled to the electrical circuit;
an input device electrically coupled to the electrical circuit; and
a software application stored in the memory device, and when executed by
the processor, the software application being adapted to provide
instructions to:
calculate a floating point answer for a mathematical operation entered for
one or more numbers entered into the computing device via the input
device,
if there is an addition and/or subtraction operation within the entered
mathematical operation,
determine the proper precision for the floating point answer based on the
entered numbers,
round the floating point answer to the proper precision,
determine the number of significant figures for the rounded answer, and
simultaneously display on the display screen the rounded answer and the
number of significant figures for the rounded answer; and
if there are no addition or subtraction operations within the entered
mathematical operation,
determine the proper number of significant figures for the floating point
answer based on the entered numbers,
round the floating point answer to the proper number of significant
figures, and
simultaneously display on the display screen the rounded answer and the
number of significant figures for the rounded answer.
20. A portable handheld calculator comprising:
a processor;
a memory device electrically coupled to the processor;
a display screen electrically coupled to the processor;
a keypad input device electrically coupled to the processor; and
a software application stored in the memory device, and when executed by
the processor, the software application being adapted to provide
instructions to:
determine the number of significant figures for a first number entered via
the keypad input device,
simultaneously display on the display screen the first entered number along
with the number of significant figures for the first entered number,
determine the number of significant figures for a second number entered via
the keypad input device,
simultaneously display on the display screen the second entered number
along with the number of significant figures for the second entered
number,
calculate a floating point answer for a mathematical operation entered,
wherein the entered numbers are the operands,
if there is an addition and/or subtraction operation within the entered
mathematical operation,
determine the proper precision for the floating point answer based on the
entered numbers,
round the floating point answer to the proper precision,
determine the number of significant figures for the rounded answer, and
simultaneously display on the display screen the rounded answer and the
number of significant figures for the rounded answer; and
if there are no addition or subtraction operations within the entered
mathematical operation,
determine the proper number of significant figures for the floating point
answer based on the entered numbers,
round the floating point answer to the proper number of significant
figures, and
simultaneously display on the display screen the rounded answer and the
number of significant figures for the rounded answer.
21. A method of displaying an answer for a mathematical operation on a
display screen of a computing device, the method comprising the steps of:
calculating a floating point answer for a mathematical operation entered
for one or more numbers entered into the computing device,
if there is an addition and/or subtraction operation within the entered
mathematical operation,
determining the proper precision for the floating point answer based on the
entered numbers,
rounding the floating point answer to the proper precision,
determining the number of significant figures for the rounded answer, and
simultaneously displaying on the display screen the rounded answer and the
number of significant figures for the rounded answer, and
if there are no addition or subtraction operations within the entered
mathematical operation,
determining the proper number of significant figures for the floating point
answer based on the entered numbers,
rounding the floating point answer to the proper number of significant
figures, and
simultaneously displaying on the display screen the rounded answer and the
number of significant figures for the rounded answer.
22. The method of claim 21, further comprising the steps of:
determining the number of significant figures for a first number entered
into the computing device;
simultaneously displaying on the display screen the first entered number
along with the number of significant figures for the first entered number;
determining the number of significant figures for a second number entered
into the computing device; and
simultaneously displaying on the display screen the second entered number
along with the number of significant figures for the second entered
number.
23. The method of claim 21, further comprising the step of:
simultaneously displaying on the display screen the floating point answer
along with the rounded answer and the number of significant figures for
the rounded answer.
24. A method of displaying an entered number on a display screen of a
computing device, the method comprising the steps of:
determining the number of significant figures for a number entered into the
computing device; and
simultaneously displaying on the display screen the entered number along
with the number of significant figures for the entered number.
25. A computer program adapted to be executed by a computing device, the
computer program comprising a method of displaying an answer on a display
screen of the computing device for a mathematical operation performed by
the computing device, the method comprising the steps of:
calculating a floating point answer for a mathematical operation entered
for one or more numbers entered into the computing device,
if there is an addition and/or subtraction operation within the entered
mathematical operation,
determining the proper precision for the floating point answer based on the
entered numbers,
rounding the floating point answer to the proper precision,
determining the number of significant figures for the rounded answer, and
simultaneously displaying on the display screen the rounded answer and the
number of significant figures for the rounded answer, and
if there are no addition or subtraction operations within the entered
mathematical operation,
determining the proper number of significant figures for the floating point
answer based on the entered numbers,
rounding the floating point answer to the proper number of significant
figures, and
simultaneously displaying on the display screen the rounded answer and the
number of significant figures for the rounded answer.
26. The computer program of claim 25, wherein the method further comprises
the steps of:
determining the number of significant figures for a first number entered
into the computing device;
simultaneously displaying on the display screen the first entered number
along with the number of significant figures for the first entered number;
determining the number of significant figures for a second number entered
into the computing device; and
simultaneously displaying on the display screen the second entered number
along with the number of significant figures for the second entered
number.
27. The computer program of claim 25, wherein the method further comprises
the steps of:
simultaneously displaying on the display screen the floating point answer
along with the rounded answer and the number of significant figures for
the rounded answer.
28. A computer program adapted to be executed by a computing device, the
computer program comprising a method of displaying an entered number on a
display screen of the computing device, the method comprising the steps
of:
determining the number of significant figures for a number entered into the
computing device; and
simultaneously displaying on the display screen the entered number along
with the number of significant figures for the entered number.
Description
FIELD OF THE INVENTION
The present invention generally relates to computing devices and more
specifically to an apparatus and method for simultaneously displaying a
number along with its number of significant figures.
BACKGROUND OF THE INVENTION
Calculators, as well as handheld computing devices, laptops, and desktop
computers, typically display the results of a mathematical operation with
as many digits as the device's display will allow. Hence, such devices
assume that entered values for the mathematical operation are exact
quantities having infinite precision. However, this assumption is
incorrect if one or more of the values entered is based on a measurement,
which has a finite precision.
For example, if the mathematical operation of 253.7.div.7.64 is entered on
a common calculator, the floating point answer displayed is 33.20680628.
Even though the first operand (253.7) has only four significant digits or
significant figures and the second operand (7.64) has only three
significant figures, the floating point answer (33.20680628) is displayed
with ten significant figures. If the first operand (253.7) and the second
operand (7.64) are both measured quantities, then the proper number of
significant figures for the answer to the mathematical operation is
three--corresponding to the least number of significant figures for the
operands in this example. In other words, the answer in this example
should be rounded to 33.2 to reflect three significant figures. Thus, a
person who does not understand the concept of significant figures may be
misled to believe that the floating point answer reflects the actual level
of precision of the answer.
As another example, if a first operand is a measured quantity of 23.625 and
the second operand is a measured quantity of 3.0125 for a mathematical
operation of 23.625+3.0125, a typical calculator will display a floating
point result of 26.6375. Note that the floating point result has a
precision to the 1/10,000 place. However, the least precise operand of the
mathematical operation is the first operand (23.625), which has a
precision to the 1/1,000 place. Hence, the properly rounded answer is
26.638--rounded to a precision of 1/1,000--corresponding to the least
precise measured value. Thus, again, a person who does not understand the
concept of rounding to the least precision for mathematical operations
involving measured values may be mislead to believe that the floating
point answer reflects the actual level of precision of the answer. Hence,
there is a need for a tool that will automatically perform the proper
rounding of an answer to a mathematical operation involving measured
values, and that will inform or remind the user that the number has been
rounded accordingly.
The concept of rounding a result of a mathematical operation to the proper
precision or to the proper number of significant figures is a known
concept. In applying the rules for rounding to the proper number of
significant figures, the following rules are used to determine the correct
number of significant figures for values in standard decimal notation (as
opposed to scientific notation described further below):
Example Number of Significant
Rule Value Figures for Example Value
Nonzero digits are always 11 2
significant. 5.759 4
Zeros between nonzero 10.05 4
digits are significant. 90005 5
Zeros in front of nonzero 0.0003 1
digits are not significant. 0.0509 3
Zeros at the end of a 23 2
number to the right of a
decimal point are significant. 23.0000 6
Zeros at the end of a 46000 2
whole number are significant
only if the decimal point 46000. 5
is shown.
The rule used to determine the correct number of significant figures for
values in scientific notation is that only significant figures are
included when writing a number in scientific notation. For example,
3.times.10.sup.6 has one significant figure, and 3.00.times.10.sup.6 has
three significant figures.
For a mathematical operation not having an addition or subtraction
operation involved, the answer to the mathematical operation is rounded to
the least number of significant figures corresponding to the measured
value in the mathematical operation having the least number of significant
figures. Such mathematical operations include multiplication and division.
Squaring (e.g., 5.sup.2 =25) operations, which are essentially
multiplication, and other operations raising a value to a power, are also
included. For example in the mathematical operation of 12.257.times.1.36
(assuming all operands are measured values), the floating point answer is
16.66952. The first operand (12.257) has five significant figures and the
second operand (1.36) has three significant figures. Hence, the operand
with the least number of significant figures is the second operand having
three significant figures. Thus, the answer rounded to the least number of
significant figures (i.e., rounded to three significant figures) is 16.7.
For a mathematical operation having an addition and/or subtraction
operation involved, the answer to the mathematical operation is rounded to
the precision of the least precise value of the measured operands. For
example in the mathematical operation of 3.95+213.6+2.879 (assuming all
operands are measured numbers), the floating point answer is 220.429. The
first operand (3.95) is precise to hundredths (1/100), the second operand
(213.6) is precise to tenths (1/10), and the third operand (2.879) is
precise to thousandths (1/1000). Hence, the least precise operand of the
mathematical operation is the second operand, which is precise to the
nearest tenth. Thus, the floating point answer (220.429) should be rounded
to the nearest tenth, which yields a rounded answer of 220.4. As another
example, 29000+6.0 (assuming each operand is a measured value) yields a
floating point result of 29006. Because the first operand (29000) is
precise to thousands (1000) and the second operand is precise to tenth
(1/10), the properly rounded answer will be 29000 (rounded to the nearest
thousands--the least precise of the mathematical operation).
For mixed mathematical operation on one or more measured values involving
addition and/or subtraction as well as multiplication, division, and/or
raising a number to a power, the final result is rounded according to the
addition and subtraction rules (least precision) described above. In such
a mixed mathematical operation, there is a default order to performing the
mathematical operations, unless another order is specified. First, the
multiplication, division, and/or raising a number to a power operations
are performed within each group separated by an addition or subtraction
operation. Second, the results of each group are added and/or subtracted
accordingly. The floating point (unrounded) result for each group is
maintained for the calculations and only the final result is rounded.
For example in the mixed mathematical operation of
12.div.4.103+2.31.times.94.8 (assuming each operand is a measured value),
the floating point answer is 221.9126893. The first operand (12) is
precise to ones and has two significant figures, the second operand
(4.103) is precise to the thousandths (1/1000) and has four significant
figures, the third operand (2.31) is precise to hundredths (1/100) and has
three significant figures, and the fourth operand (94.8) is precise to the
tenths (1/10) and has three significant figures. Thus the properly rounded
answer (according to the least precise operand--the first operand) is 222,
which is precise to the nearest ones and happens to have three significant
figures. Therefore, the answer is rounded to the nearest ones according to
the addition and subtraction rules, and the answer has three significant
figures, even though the least number of significant figures among the
operands was two significant figures.
When an exact value is involved in a mathematical operation, its number of
significant figures does not affect the proper rounding of the answer. For
example, in taking the average of three measured values 3.473, 23.937, and
102.54, the sum of these values is divided by three because there are
exactly three values being averaged. Hence, the operand 3 in the
mathematical operation does not affect the resulting precision of the
properly rounded answer because it is an exact number. Hence, the
resulting answer should be rounded to the nearest hundredths (1/100)
because the least precise measured value (102.54) is precise to
hundredths. Therefore, the properly rounded answer is 43.32. Note that
these methods of rounding the result of a mathematical operation based on
the significant figures and/or precision of the operands are merely
conventions to express results with the appropriate precision based upon
the precision of the measured values, rather than firm rules. Hence, these
methods may vary slightly.
Because these rules for rounding an answer for a mathematical operation
involving one or more measured values are more easily understood through
examples, there is a need for an education tool that will display the
number of significant figures for each operand entered. Such a display can
illustrate to the user, or reassure the user, of the number of significant
figures for each operand, which may aid in the education process. Also,
there is a need for an education tool that will determine and display a
properly rounded answer to a mathematical operation involving one or more
measured values. Such a tool can illustrate or reassure the user of the
properly rounded answer, which may also aid in the educational process.
BRIEF SUMMARY OF THE INVENTION
The problems and needs outlined above are addressed by the present
invention. In accordance with one aspect of the present invention, a
computing device is provided. The computing device comprises an electrical
circuit, a display screen, an input device, and a software application.
The electrical circuit comprises a processor and a memory device
electrically coupled to the processor. The display screen and the input
device are electrically coupled to the electrical circuit. The software
application is stored in the memory device. When executed by the
processor, the software application is adapted to provide instructions to
determine the number of significant figures for a number entered via the
input device, and simultaneously display on the display screen the entered
number along with the number of significant figures for the entered
number.
The computing device may be a calculator. For a calculator, the display
screen may comprise a liquid crystal display device, and the input device
may comprise a keypad on the calculator. The computing device may be a
handheld portable computing device. For a handheld portable computing
device, the display screen may comprise a liquid crystal display device,
an active matrix display device, or a touch sensitive screen. For a
handheld portable computing device with a touch sensitive screen, the
input device may comprise a simulated keypad displayed on the touch
sensitive screen so that a user can input a number or mathematical
operator by contacting the touch sensitive screen with a touch wand or a
finger. The computing device may be a laptop computer or a desktop
computer. For a desktop computer, the display screen may comprise a
cathode ray tube device, and the input device may comprise a keyboard
device. The display screen may comprise a television. The computing device
may comprise a server and a terminal, and the computing device may be
structured in an application service provider (ASP) model such that the
terminal is remotely located from the server, the display screen and input
device are parts of the terminal, the electrical circuitry is part of the
server, and the display screen and input device are electrically coupled
to the electrical circuit via a network connection. The network connection
may comprise the Internet and/or a local area network (LAN). The memory
device may comprise a flash memory device, a hard drive, and/or a
synchronous dynamic access memory (SDRAM) device.
The software application may be further adapted to provide instructions to
determine the number of significant figures for a second number entered
via the input device, and simultaneously display on the display screen the
second entered number along with the number of significant figures for the
second entered number. Also, the software application may be adapted to
provide instructions to calculate a floating point answer for a
mathematical operation entered, wherein the entered numbers are the
operands, determine the proper number of significant figures for the
floating point answer based on the number of significant figures for each
of the operands, round the floating point answer to the proper number of
significant figures for the answer, and simultaneously display on the
display screen the rounded answer along with the number of significant
figures for the rounded answer. Furthermore, the software application may
be further adapted to provide instructions to simultaneously display the
floating point answer on the display screen along with the rounded answer
and the number of significant figures for the rounded answer. Also, the
software application may be adapted to provide instructions to calculate a
floating point answer for a mathematical operation entered, wherein the
entered numbers are the operands, determine which of the operands is least
precise, round the floating point answer to least precision of the
operands, determine the number of significant figures for the rounded
answer, and simultaneously display on the display screen the rounded
answer along with the number of significant figures for the rounded
answer.
In accordance with another aspect of the present invention, a computer
program adapted to be executed by a computing device is provided. The
computer program comprises a method of displaying an answer for a
mathematical operation on a display screen of a computing device. The
method comprises the following steps, the order of which may vary:
calculating a floating point answer for a mathematical operation entered
for one or more numbers entered into the computing device, (i) if there is
an addition and/or subtraction operation within the entered mathematical
operation, determining the proper precision for the floating point answer
based on the entered numbers, (a) rounding the floating point answer to
the proper precision, (b) determining the number of significant figures
for the rounded answer, and (c) simultaneously displaying on the display
screen the rounded answer and the number of significant figures for the
rounded answer, and (ii) if there are no addition or subtraction
operations within the entered mathematical operation, (a) determining the
proper number of significant figures for the floating point answer based
on the entered numbers, (b) rounding the floating point answer to the
proper number of significant figures, and (c) simultaneously displaying on
the display screen the rounded answer and the number of significant
figures for the rounded answer.
The method may further comprise the steps of: (iii) determining the number
of significant figures for a first number entered into the computing
device; (iv) simultaneously displaying on the display screen the first
entered number along with the number of significant figures for the first
entered number; (v) determining the number of significant figures for a
second number entered into the computing device; and (vi) simultaneously
displaying on the display screen the second entered number along with the
number of significant figures for the second entered number. Also, the
method may further comprise the step of simultaneously displaying on the
display screen the floating point answer along with the rounded answer and
the number of significant figures for the rounded answer.
In accordance with yet another aspect of the present invention, a computer
program adapted to be executed by a computing device is provided, wherein
the computer program comprises a method of displaying an entered number on
a display screen of a computing device. The method comprises the following
steps: (i) determining the number of significant figures for a number
entered into the computing device; and (ii) simultaneously displaying on
the display screen the entered number along with the number of significant
figures for the entered number.
BRIEF DESCRIPTION OF THE DRAWINGS
Other objects and advantages of the invention will become apparent upon
reading the following detailed description and upon referencing the
accompanying drawings, in which:
FIG. 1 is a drawing of a calculator in accordance with a preferred
embodiment of the present invention;
FIG. 2 is a flowchart showing a main process logic and instructions
provided by a software application for the calculator of FIG. 1;
FIG. 3 is a flowchart showing a subroutine of the main process of FIG. 2
for computing the significant figures of a number;
FIG. 4 is a flowchart showing a subroutine of the main process of FIG. 2
for rounding an answer and computing the significant figures for the
rounded answer; and
FIGS. 5-24 are screenshots from the calculator of FIG. 1 to illustrate some
of the various uses of the preferred embodiment in accordance with the
present invention.
DETAILED DESCRIPTION OF THE INVENTION
Referring now to the drawings, wherein like reference numbers are used
herein to designate like elements throughout the various views, a
preferred embodiment of the present invention is illustrated and
described, and other possible embodiments of the present invention are
described. The figures are not necessarily drawn to scale, and in some
instances the drawings have been exaggerated and/or simplified in places
for illustrative purposes only. One of ordinary skill in the art will
appreciate the many possible applications and variations of the present
invention based on the following examples of possible embodiments of the
present invention.
The present invention provides a way to determine the number of significant
figures for a number entered via the input device, and to simultaneously
display on a display screen the entered number along with the number of
significant figures for the entered number. In another aspect, the present
invention provides a way to properly round an answer to a mathematical
operation involving one or more measured values according to the precision
or number of significant figures of operands that are measured, and to
simultaneously display the rounded answer along with the number of
significant figures for the rounded answer.
The following description and FIGS. 1-24 pertain to a preferred embodiment
of the present invention. FIG. 1 illustrates the preferred embodiment
discussed herein, which is a portable, handheld calculator 40 having a
software application loaded in its memory. In this example, the calculator
40 is a TI-83 Plus produced by Texas Instruments, Inc. However, the
present invention may be incorporated into a different model and/or a
calculator made by another company. The preferred embodiment discussed
herein is but one illustrative example of the use of the present invention
and does not limit the scope of the invention to the preferred embodiment
described. The present invention may be embodied in many different
computing devices. For example, the present invention may be a software
application adapted to run on (but is not limited to) a desktop computer
(not shown), a palm-size computing device (not shown), a laptop computer
(not shown), or a server connected to a terminal via a network connection
(not shown).
FIGS. 2-4 are pseudo code flowcharts illustrating the process logic and
instructions provided by the software application for the preferred
embodiment. The particular computer language used to implement the logic
and instructions shown in FIGS. 2-4 may vary, depending on the
programmer's preference and/or depending on the computing device of an
embodiment. FIG. 2 illustrates the main process 42. FIGS. 3 and 4
illustrates subroutines 44, 46 called upon by the main process 42.
Beginning in FIG. 2 at the start block 48 of the main process 42, the
software waits for a user to enter a number (block 50). While inputting a
number, the user may indicate whether the entered number is an exact
number (infinite precision) or a measured value (limited precision). The
default is to assume the number entered is a measured value, unless the
user indicates otherwise. However, such default could be reversed to make
an exact number the default, which is what most conventional calculators
are limited to. If the user pressed the EXACT soft key 52 (shown in FIG.
5), the exact indicator is displayed on the screen along with the entered
number (e.g., see FIG. 7). The EXACT key 52 may be pressed at any time
while the user inputs the number (i.e., before, during, or after entering
the complete number). The software also waits for an operation key to be
pushed to signify the completion of entering the number (block 54). In the
preferred embodiment, the operation keys include: ENTER, .times., .div.,
^, -, and +. When an operation key is pressed, and thus the complete
number has been entered, the number of significant figures for the entered
number is computed (subroutine block 56).
The "compute significant figures of number" block 56 refers to the
subroutine flowchart 44 of FIG. 3. At the start (block 58) of the FIG. 3
flowchart, the first character of the entered number is evaluated. Also,
the SigFig count variable and the potential SigFig count variable are each
set to zero as an initialization (action block 60). The first character is
evaluated to determine whether it is a "-" sign (decision block 62). If
the first character is a "-" sign (negative sign indicating negative
number), the next character of the entered number is evaluated. If the
first character is not a "-" sign, it is then evaluated to determine
whether it is an "E" character (decision block 64), which is used for
scientific notation to represent ".times.10.sup.y," where y is the number
following "E." If the first character is not an "E," it is next determined
whether the first character is a zero (decision block 66). If the first
character is not a zero, it is then determined whether it is the end of
the string indicator (decision block 68). If the end of string is not
reached, the entered number is evaluated to determine whether a decimal
point has been encountered yet (decision block 70). If a decimal point has
been encountered already within the string of the entered number, the
potential SigFig count variable is added to the SigFig count variable
(action block 72). Then, the SigFig count variable is set to zero (action
block 74). If a decimal point has not been encountered yet (decision block
70), the SigFig count variable is set to zero (action block 74).
Next, the first character is evaluated to determine whether it is a decimal
point (decision block 76). If the first character is a decimal point, the
software notes or registers that a decimal point has been encountered
(action block 78). Then, the next character of the entered number is
retrieved for evaluation (action block 80). If the first character is not
a decimal point (decision block 76), the SigFig count variable is
incremented by one (action block 82), and then the next character is
retrieved for evaluation (action block 80).
Referring back to the "Is character a "0"?" decision block 66, if the first
character is a zero, then the SigFig count variable is evaluated to
determine whether the SigFig count is greater than zero (decision block
84). If the SigFig count is greater than zero, then the potential SigFig
count is incremented by one (action block 86), and then the next character
is retrieved for evaluation (action block 80). If the SigFig count is not
greater than zero (decision block 84), then the next character is
retrieved for evaluation (action block 80).
Referring back to the "Is character an "E"?" decision block 64, if yes and
the first character is an "E," then the SigFig count is evaluated to
determine whether it equals zero (decision block 88). If the SigFig count
variable does not equal zero, then it is determined whether there was a
decimal point already (decision block 90). If there was already a decimal
point, the potential SigFig count is added to the SigFig count (action
block 92), and then the subprogram is finished (block 94) and returns to
the main process 42 (FIG. 2) at block 56 with the value in the SigFig
count variable, which is the computed number of significant figures for
the entered number. Backing up one step to decision block 90 in FIG. 3, if
there was not a decimal point encountered, then the subprogram is finished
(block 94) and returns to the main process 42 (FIG. 2) at block 56 with
the value in the SigFig count variable. However, backing up two steps to
decision block 88 in FIG. 3, if the SigFig count equals zero, the
character is evaluated to determine whether it is the first character
(decision block 96). If it is the first character, the SigFig count
variable is set to equal one (action block 98). If the currently evaluated
character is not the first character (decision block 96), then the "Was
there a decimal point?" decision block 90 is performed (as described
above).
Referring back to the "End of string?" decision block 68 in FIG. 3, if the
end of string is encountered, then the "Was there a decimal point?"
decision block 90 is performed (as described above). At this point, all
flow routes for the FIG. 3 subroutine flowchart 44 have been described.
Referring again to the main process 42 of FIG. 2, after the number of
significant figures for the entered number is determined (block 56), it is
determined whether the user presses the EXACT soft key (decision block
100). This step is needed because the user may have edited the entered
number and during such editing pressed the EXACT soft key. If the EXACT
key was not pressed, the number of significant figures for the entered
number is displayed on screen simultaneously with the entered number
(display action block 102).
This simultaneous display of the entered number along with its number of
significant figures (block 102) provides information that may educate,
reassure, or remind the user of the number of significant figures for the
entered number. Such information may be a valuable in teach a student, for
example, about significant figures by allowing the student to enter
examples into the calculator 40. Also, such information may be valuable as
a self-teaching aid or as a reminder for a person trying to learn about or
refresh his/her memory regarding significant figures.
After displaying the number of significant figures for the entered number
(block 102), or after it is determined in decision block 100 that the user
did press the EXACT soft key, it is determined whether the operation was
an ENTER operation (decision block 104) (i.e., the user pressed the ENTER
key on the calculator (see FIG. 1) after inputting the number). If the
operation is not an ENTER operation, the operation character is displayed
(display action block 106), and then the software waits for the next
number or operand to be input by the user (block 50). If the operation is
an ENTER operation (decision block 104), the calculator 40 computes the
floating point answer (action block 108). Because the computation of a
floating point answer by a computing device for mathematical operations is
well known to those of ordinary skill in the art, the details of this
process are not described herein.
After the floating point answer is computed (action block 108), it is
displayed on the screen (display action block 110). Next (or simultaneous
to the computation of the floating point answer), the number of
significant figures for the answer is determined (subroutine block 112).
The "compute significant figures for answer" block 112 refers to the
subroutine flowchart 46 of FIG. 4. At the start (block 114) of the FIG. 4
flowchart, the individual operators for the mathematical operation are
evaluated to determine whether there are any multiplication, division,
and/or to the power of operations (decision block 116). If there are no
multiplication, division, or to the power of operations (e.g., only
addition and/or subtraction operations), it is determined whether there is
more than one group (decision block 118). That is, the mathematical
operation is divided into "groups" separated by addition or subtraction
operations ("groups" correlate to the mathematical concept of "terms").
For example in the mathematical operation of 3.452+5.93-1.007, there will
be three "groups" ((3.452)+(5.93)-(1.007)): the first "group" being
(3.452), the second "group" being (5.93), and the third "group" being
(1.007). The grouping becomes more relevant with mixed mathematical
operations (discussed below). Hence, in the case where there are no
multiplication, division, or to the power of operations, it is unlikely
that there will not be more than one group.
When there is more than one "group" (decision block 118), the next step is
to determine the precision of each "group" (action block 120). Next the
least precise group is identified and noted (action block 122). Then, the
addition and/or subtraction operations are performed on the groups
resulting in a floating point answer (action block 124) (note: this step
may occur while computing the floating point answer or it may be performed
again for the purpose of obtaining the rounded answer). Next, the floating
point answer is rounded to match the precision of the least precise group
(action block 126). For example, if the least precise group is precise to
the tenths (1/10), then the floating point answer is rounded to the
nearest tenths place.
Next, the number of significant figures for the rounded answer is
determined (subroutine block 56), which may be performed using the process
44 of FIG. 3. At this point for this route through the FIG. 4 flowchart
46, the FIG. 4 subroutine 46 is finished and the rounded answer and its
number of significant figures are returned to the main process 42 of FIG.
2.
Referring back to the "Were there any *, /, or ^ operations" decision
block 116 of FIG. 4, if yes and there is a multiplication, division,
and/or to the power of operation in the mathematical operation, the next
step is to group each set of contiguous multiplication, division, and/or
to the power of operations (action block 128). That is, as described
above, the mathematical operation is divided into "groups" separated by
addition or subtraction operations. For example in the mathematical
operation of 5.23.sup.2.times.3.14159+0.93/2.5-1.007, there will be three
"groups" ((5.23^2.times.3.14159)+(0.93/2.5)-(1.007)): the first
"group" being (5.23^2.times.3.14159), the second "group" being
(0.93/2.5), and the third "group" being (1.007). Then, the operations for
each group are separately performed (action block 130). For each group the
smallest number of significant figures among the group's operands is
determined and stored along with the floating point result for that group
(note: this step may occur within or in addition to the step of computing
the floating point answer (computation block 108) shown in FIG. 2). This
step is repeated until all the groups are processed (see "Are there more
groups?" decision block 132 and "Look at next group" action block 134 in
FIG. 4).
Note that there may be only one group. For example in the mathematical
operation of 6.834.sup.2.times.3.14159, there is only one group because
there are no addition or subtraction operations. After all the groups are
processed, the next step is the "Is there more than one group" decision
block 118, which was described above. At this point, if there is more than
one group (i.e., it is a mix mathematical operation also having addition
and/or subtraction operations), the mathematical operation is essentially
the same as that described above for the case of addition and/or
subtraction only. In other words, because all of the multiplication,
division, and/or to the power of operations for each "group" have already
been performed, the mathematical operation is reduced to addition and/or
subtraction operations, which have been described above. If there is only
one group, the floating point answer for that group is rounded to the
smallest number of significant figures stored for that group in a prior
step 130 (action block 136). At the end of the FIG. 4 process flow 46, in
either case, the properly rounded answer along with its number of
significant figures is returned to the main process 42 of FIG. 2.
Note that the "Compute Floating Point answer" block 108, the "Display
Floating Point answer" block 110, and the "Compute Significant Figures for
Answer" block 112 of FIG. 2 may vary in their respective order and/or may
be performed simultaneously and/or integrally. Likewise, as will be
apparent to one of ordinary skill in the art in light of this disclosure,
the order of the steps for any of the processes of FIGS. 2-4 may vary or
may become integrated in a variety of equivalent ways to perform the same
core functions to achieve the same results.
Referring to FIG. 1 again, the calculator 40 of the preferred embodiment is
just one example of a computing device having a software application in
accordance with the present invention. As is well known to those of
ordinary skill in the art, a computing device, such as a calculator or a
personal computer for example, comprises (but is not limited to) an
electrical circuit 137 having a processor 139 electrically coupled to a
memory device 141, as well as a display screen 138 and an input device 140
electrically coupled to the electrical circuit. For illustration purposes,
the electrical circuit 137 is shown schematically outside of the
calculator 40, even though the electrical circuit 137 is actually within
and a part of the calculator 40 in this example. A computing device also
comprises at least one software application stored in the memory device
141 that is adapted to be executed by the processor 139. The processor
139, memory device 141, display screen 138, input device 140, and software
application, each may vary for a given application. Consider the following
examples illustrating some variations of these components for a variety of
computing devices, which are just a few examples and are not intended to
limit the scope of a claimed invention herein.
As shown in FIG. 1, a computing device may be a portable, handheld-size
scientific calculator 40. Such a calculator 40 may be battery powered,
solar powered, and/or powered by an AC/DC converter that can be plugged
into an AC wall outlet. In FIG. 1, the display screen 138 of the
calculator 40 has a liquid crystal display (LCD). The memory device 141
comprises a flash memory device, which stores the software application,
among other tasks. The input device 140 comprises a keypad device with a
variety of buttons. The input device also comprises "soft keys" 142, which
are buttons 144 whose function may change to suit a given software
application. For example, in FIG. 5, five soft keys 142 are displayed on
the screen 138. If the user presses a button 144 below the displayed soft
key 142, it will provide the input displayed on the soft key 142. Hence in
FIG. 5, if a user presses the button 146 below the EXACT soft key 148,
such button depression will be interpreted by the software application as
the user's desire to designate the number being entered as an exact value
(i.e., not a measured value--infinite precision).
As another example, the computing device may be a desktop computer (not
shown) with a cathode ray tube monitor (not shown) as the display screen
and with a standard keyboard (not shown) as the input device. For the
desktop computer, the processor 139 may be a Texas Instruments.RTM. DSP
chip, an Intel.RTM. Pentium.RTM. microprocessor, or an AMD.RTM.
Athion.RTM. microprocessor, for example. The memory device 141 may be a
double data rate (DDR) synchronous dynamic random access memory (SDRAM)
memory module (not shown) and/or a magnetic hard drive device (not shown),
each electrically coupled to an electrical circuit, which in this case
comprises a motherboard (not shown). The computing device may be adapted
to connect to a television (not shown), so that the television provides a
display screen.
Similarly, the computing device may be a laptop personal computer (not
shown), a palm-size computing device (not shown), or in general, handheld
portable computing device. The display screen may comprise a LCD device or
an active matrix display device (not shown). The display screen and the
input device may be integral with one another. For example, if the display
screen comprises a touch sensitive screen (not shown) that allows inputs
to be received by touching the screen with a finger or a touch wand (not
shown), the input device may be a simulated keypad displayed on the touch
sensitive screen. Such displays are often used in portable palm-sized
computer devices for example.
The present invention may also be embodied in an computing device
structured as an application service provider (ASP) model. For example, a
server (not shown) may provide an electrical circuitry that comprises the
processor, memory, and software application. A terminal (not shown),
located remotely from the server and connected to the server via a network
connection (not shown), may provide the display screen (e.g., monitor,
television) and input device (e.g., mouse, keyboard, keypad device).
Hence, the software application at the server may receive the number
inputs from a user at the input device of the remote terminal via a
network connection. Then, the server may send the results and display
information to be displayed at the remote terminal via the network
connection. The network connection may comprise a local area network
(LAN), a wide area network (WAN), the Internet, and/or a dedicated phone
line. The network connection may also be a secure connection using
encryption technology to encrypt and decrypt the packets of data.
FIGS. 5-24 are screenshots from the calculator embodiment 40 of FIG. 1
having the software application described in the flowcharts 42, 44, and 46
of FIGS. 2-4. The screenshots of FIGS. 5-24 illustrate the display shown
to a user while using the calculator 40 of the preferred embodiment for
various example mathematical operations. The following examples will
briefly describe the actions of a user and the results provided by the
calculator embodiment 40 to illustrate the some uses of the preferred
embodiment of the present invention. The detailed steps described above
for the flowcharts 42, 44, and 46 of FIGS. 2-4 correspond to the
instructions and logic provided by the software application and performed
by the processor within the calculator to provide the displayed results.
FIG. 5 shows an example of a mathematical operation having multiplication
only. To perform the mathematical operation of FIG. 5, the user first
inputs the measured value of 120.1 into the calculator via the key pad 140
(see FIG. 1), then the user presses the multiplication operation button
(.times.). At this point the calculator determines the number of
significant figures for the first entered number and displays the number
of significant figures for the first entered number, as well as the
multiplication operator (*) (see FIG. 5). Next the user inputs the second
operand, which is a measured value of 3.55, and then presses the ENTER
button on the keypad. Now the calculator computes the floating point
answer for the mathematical operation, which is 426.355. Also, the
calculator computes the properly rounded answer (426) and its number of
significant figures (3). The rounded answer and its number of significant
figures are then displayed together on the screen simultaneously. FIG. 5
is the resulting screenshot at the conclusion of the mathematical
operation. Note that of the two measured value operands in this case, the
least number of significant figures was three, and hence the floating
point answer was rounded to three significant figures in accordance with
the rules for rounding to the proper number of significant figures (rules
described above in the Background section).
FIG. 6 shows an example of a mathematical operation having division only.
To perform the mathematical operation of FIG. 6, the user first inputs the
measured value of 22.6875 into the calculator 40 via the key pad 140 on
the calculator, then the user presses the division operation button
(.div.). At this point the calculator 40 determines the number of
significant figures for the first entered number and displays the number
of significant figures for the first entered number, as well as the
division operator (/) (see FIG. 6). Next the user inputs the second
operand, which is a measured value of 3.575, and then presses the ENTER
button on the keypad 140. Now the calculator 40 computes the floating
point answer for the mathematical operation, which is 6.346153846. Also,
the calculator computes the properly rounded answer (6.346) and its number
of significant figures (4). The rounded answer and its number of
significant figures are then displayed together on the screen 138
simultaneously. FIG. 6 is the resulting screenshot at the conclusion of
the mathematical operation. Note in this case that of the two measured
value operands, the least number of significant figures was four, and
hence the floating point answer was rounded to four significant figures in
accordance with the rules for rounding to the proper number of significant
figures.
FIG. 7 shows an example with multiplication and division, but note that the
third operand (3) is an exact value. Because the default for this
embodiment is that each number entered is a measured value, the user must
press the EXACT soft key sometime after pressing the division button
(.div.) and before pressing the ENTER button when inputting the third
operand in the keypad 140 to inform the calculator 40 that this is an
exact value. Thus, when computing the properly rounded answer (9.64), the
number of significant figures for the third operand does not affect the
rounding of the floating point answer. In other words, note in this case
that of the two measured value operands (2.037 and 14.2), the least number
of significant figures was three, and hence the
