; BinaryCounter
; written by Teresa Carrigan, 2004
globals [ start-x high-bit eq-unsign eq-sign eq-ones eq-twos praise]
breeds [ arrow ]
arrow-own [ state ]
patches-own [ place-value current-value name ]
; runs setup when program is first loaded
to startup
setup
end
; makes the correct number of bits, and the red arrow
; initializes variables
to setup
locals [ here-x current ]
ca
set praise [ "You got it!" "Right!" "Correct" "Awesome!" "Perfect!" ]
set start-x 7
set here-x 4
ask patch-at (here-x + 1) 0 [set pcolor white]
set current 1
set eq-unsign 0
set eq-sign 0
set eq-ones 0
set eq-twos 0
; for each bit
repeat number-of-bits [
ask patch-at here-x 0
[
set pcolor white
set plabel "0"
set plabel-color black
set here-x (here-x - 1)
set place-value current
]
set high-bit (current - 1)
set current (current * 2)
]
; create red arrow
cct-arrow 1 [
setxy start-x 0
set heading -90
set color red
set shape "arrow"
set state "done"
]
; create explanation bar at the bottom
ask patches with [ pycor < -3 ]
[ set pcolor blue ]
ask patch-at 6 -4
[ set plabel "Counting in Binary "
set plabel-color white
set name 1
]
ask patch-at 6 -5
[ set plabel ""
set name 2
]
end
; add one to the bit pattern
to increment
set state "add"
wait slow-motion
ifelse plabel = "0"
[
set plabel "1"
set current-value place-value
ask patches with [name = 2 ]
[ set plabel "Change 0 to 1 - done!" ]
go-back
]
[
ifelse plabel = "1"
[ set plabel "0"
set current-value 0
fd 1
ask patches with [name = 2 ]
[ set plabel "Change 1 to 0, keep going." ]
increment
]
[ ; check for past left-most bit
ifelse xcor < 0
[
ask patches with [name = 2 ]
[ set plabel "Overflow!!!" ]
go-back
]
[ fd 1
increment
]
]
]
end
; return red arrow to starting position
to go-back
set state "return"
calc
rt 90
fd 5
wait slow-motion
rt 90
set xcor start-x
wait slow-motion
rt 90
fd 5
wait slow-motion
rt 90
set state "done"
end
; update monitors
to calc
calc-unsigned
calc-signed
calc-ones
calc-twos
end
; decimal equivalent if unsigned binary
to calc-unsigned
set eq-unsign (sum values-from patches [ current-value ])
end
; decimal equivalent if two's complement
to calc-twos
locals [ allones neg ]
set neg (sum values-from patches [ current-value ])
ifelse neg <= high-bit
[
set eq-twos neg
]
[
set allones (sum values-from patches [ place-value ])
set eq-twos (neg - allones - 1)
]
end
; decimal equivalent if one's complement
to calc-ones
locals [ allones neg ]
set neg (sum values-from patches [ current-value ])
ifelse neg <= high-bit
[
set eq-ones neg
]
[
set allones (sum values-from patches [ place-value ])
set eq-ones (neg - allones)
]
end
; decimal equivalent if signed magnitude
to calc-signed
locals [ fixsign neg ]
set neg (sum values-from patches [ current-value ])
ifelse neg <= high-bit
[
set eq-sign neg
]
[
set fixsign (high-bit + 1)
set eq-sign (neg - fixsign) * -1
]
end
; randomizes the bits showing
to random-bits
ask patches with [ plabel = "0" or plabel = "1" ]
[
set plabel random-one-of [ "0" "1" ]
ifelse plabel = "0"
[ set current-value 0 ]
[ set current-value place-value ]
]
end
; asks a quiz question involving counting
to ask-count
locals [ guess target question]
without-interruption [ set question get-number ]
set question add-commas question
set guess user-input (word "What is one more than " question "?")
set guess (word " " guess " ")
set guess remove " " guess
set guess remove "," guess
ask turtles
[ go-back
increment
]
without-interruption [ set target get-number ]
ifelse guess = target
[ user-message random-one-of praise ]
[ set target add-commas target
user-message "I'm sorry, but the correct answer is " + target]
end
; asks a quiz question involving data representation
to ask-other [qt]
locals [ guess target question ]
without-interruption [ set question get-number ]
set question add-commas question
set guess user-input (word "Convert the " qt " number " question " to decimal.")
set guess remove " " guess
set guess remove "," guess
set guess read-from-string guess
without-interruption [ calc ]
ifelse member? "unsign" qt
[ set target eq-unsign]
[ ifelse member? "sign" qt
[ set target eq-sign]
[ ifelse member? "one" qt
[ set target eq-ones]
[ set target eq-twos]
]
]
ifelse guess = target
[ user-message random-one-of praise ]
[ user-message "I'm sorry, but the correct answer is " + int target + "."]
end
; read the bits on the patches, storing it as a string
to-report get-number
locals [ target ]
set target ""
ask turtles
[ while [ xcor > 0 or pcolor = white ]
[ if plabel = "0" or plabel = "1"
[ set target word plabel target ]
fd 1
]
go-back
]
set target remove " " target
report target
end
; add commas every three bits, so the user won't make copy errors
to-report add-commas [ number ]
locals [ save k ]
set save ""
set k 0
while [ (length number) > 0 ]
[
set save (word last number save )
set number butlast number
set k (k + 1)
if (k = 3) and (length number > 0)
[ set save (word "," save )
set k 0
]
]
set number save
report number
end
; ask a quiz question - calls ask-counting or ask-other
to quiz
locals [qt flag]
ask arrow [ set flag state ]
ifelse flag = "done"
[without-interruption [random-bits ]
wait .5
ifelse quiz-topic = "random"
[ set qt random-one-of ["counting" "signed binary" "unsigned binary" "one's complement" "two's complement"] ]
[ set qt quiz-topic ]
ifelse qt = "counting"
[ ask-count ]
[ ask-other qt ]
]
[
user-message "No quiz until arrow stops."
]
end
; *** NetLogo Model Copyright Notice ***
;
; Copyright 2004 by Teresa W. Carrigan. All rights reserved.
;
; Permission to use, modify or redistribute this model is hereby granted,
; provided that both of the following requirements are followed:
; a) this copyright notice is included.
; b) this model will not be redistributed for profit without permission
; from Teresa W. Carrigan.
; Contact Teresa W. Carrigan for appropriate licenses for redistribution
; for profit.
;
; To refer to this model in academic publications, please use:
; Carrigan, T. (2004). Binary Counter model.
; Blackburn College, Carlinville IL.
;
; In other publications, please use:
; Copyright 2004 by Teresa W. Carrigan. All rights reserved.
;
; *** End of NetLogo Model Copyright Notice ***
@#$#@#$#@
GRAPHICS-WINDOW
3
10
388
316
7
5
25.0
1
18
1
1
1
CC-WINDOW
393
261
607
322
Command Center
BUTTON
416
42
588
75
NIL
setup
NIL
1
T
OBSERVER
T
BUTTON
417
75
503
108
NIL
increment
NIL
1
T
TURTLE
T
SLIDER
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589
177
number-of-bits
number-of-bits
2
10
5
1
1
bits
BUTTON
503
75
587
108
loop
increment
T
1
T
TURTLE
T
SLIDER
417
109
590
142
slow-motion
slow-motion
0
1
0.25
0.05
1
seconds
MONITOR
4
318
111
367
if unsigned binary
eq-unsign
0
1
MONITOR
112
318
213
367
if signed binary
eq-sign
0
1
MONITOR
214
318
337
367
if one's complement
eq-ones
0
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MONITOR
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464
367
if two's complement
eq-twos
0
1
BUTTON
392
179
617
212
QUIZ
quiz
NIL
1
T
OBSERVER
T
CHOICE
392
214
617
259
quiz-topic
quiz-topic
"counting" "unsigned binary" "signed binary" "one's complement" "two's complement" "random"
5
@#$#@#$#@
WHAT IS IT?
-----------
This model demonstrates counting in binary, and gives the decimal equivalent of the bit pattern for various data representations. This demonstration will help you understand integer overflow and the problems it can cause when undetected. It can also ask you questions, to see how well you understand the concepts.
HOW IT WORKS
------------
Each time the binary number is incremented, the red arrow passes to the left. When it finds a 1, it changes the 1 to a 0 but continues to the left. When it finds a 0, it changes the 0 to a 1 and returns to the start position.
Each patch holding either a 0 or a 1 has two variables. The place-value is the decimal amount that a 1 in that position would have. The right-most place value is 1, the next is 2, the third is 4, etc. with each place-value doubling the one on its immediate right. The current-value of a patch will equal the place-value if the patch shows a 1, and equal zero otherwise.
If a bit pattern is stored using unsigned binary, then the decimal equivalent is the sum of all the current-values of the patches. For the other three representations, if the left-most bit is zero then the decimal equivalent is the same as if it were unsigned binary. When the left-most bit is one, then the decimal equivalent will be negative, and each representation gives a different result.
Assuming the left-most bit is one, the signed magnitude equivalent is calculated by adding the current-values of all the patches except the left-most one, and then making that sum negative.
If the left-most bit is one, then the one's complement equivalent is calculated by adding the current-values of all the patches (including the left-most one), and then subtracting the sum of all the place-values of the patches.
The two's complement equivalent is always one less (more negative) than the one's complement, when the left-most bit is a one.
HOW TO USE IT
-------------
Use the number-of-bits slider to set the number of bits that the counter can hold. Now press the setup button to change the number of bits displayed. This will zero all the bits.
The slow-motion slider is an easy way to adjust the speed of the display so you can watch the bits change as the red arrow moves. Set it to zero if you want to quickly count to a large number.
The increment button adds one to the bit pattern, using rules that work well when the number is positive.
The loop button will continuously increment the counter until clicked a second time.
The four monitors display the decimal equivalent of the bit pattern, assuming that the bits have been stored using each of the four different data representations.
To take a quiz, first select the quiz topic, and then click the quiz button. You may choose to include commas or spaces in your answer to help you count digits; they will be ignored. If you choose "random" for your quiz topic, then one of the other possible quiz topics will be chosen for you.
THINGS TO NOTICE
----------------
Watch the decimal equivalent monitors while you count. Notice that when the left-most bit is zero, they all agree, but when the left-most bit is one, they all disagree. Is that always the case? Can you find a case where the signed magnitude agrees with either one's complement or two's complement, but not the others?
Determine algebraic expressions between the different equivalents. One's complement and two's complement are easy.
What is the range of possible values for the different equivalents? Determine algebraic expressions for the ranges, in terms of the number of bits.
THINGS TO TRY
-------------
Set the slow-motion to about .10 seconds (or slower) and press the increment button a few times. Watch the red arrow change bits, and notice when it decides no more bits need to be changed.
What happens when all the bits are one, and you increment again?
What happens to the decimal equivalents when all the bits except the left-most one are one, and you increment again?
EXTENDING THE MODEL
-------------------
Modify the model to show fixed point binary representation; that is, specify a given number of bits to the right of the decimal place.
Allow the user to input a starting bit pattern.
Allow the user to input a decimal number, and then display the corresponding bit patterns for each of the four data representations.
NETLOGO FEATURES
----------------
"sum values-from patches" is used to easily add all the current value of each patch.
The startup procedure is used to automatically call setup when the program is opened.
"to-report" is used to read the binary number off the patches, and to add commas to a string of bits.
RELATED MODELS
--------------
Counting in Other Number Bases; Place Value Method; Horner's Method; Binary, Quaternary, Octal, Hexadecimal
CREDITS AND REFERENCES
----------------------
This model was written by Teresa W. Carrigan, 2004.
Permission to use, modify or redistribute this model is hereby granted,
provided that both of the following requirements are followed:
a) this copyright notice is included.
b) this model will not be redistributed for profit without permission
from Teresa W. Carrigan.
Contact Teresa W. Carrigan for appropriate licenses for redistribution
for profit.
To refer to this model in academic publications, please use:
Carrigan, T. (2004). Binary Counter model.
Blackburn College, Carlinville, IL.
In other publications, please use:
Copyright 2004 by Teresa W. Carrigan. All rights reserved.
FOR MORE INFORMATION
----------------------
For more information on data representation such as two's complement, see one of these textbooks:
[1] Null, L. and Lobur, J. "Essentials of Computer Organization and Architecture", First Edition, Jones and Bartlett, pages 38-55.
[2] Dale, N. and Lewis, J. "Computer Science Illuminated", Second Edition, Jones and Bartlett, pages 59-62.
[3] Stallings, W. "Computer Organization and Architecture: Designing for
Performance", Sixth Edition, Prentice Hall, pages 286-290.
[4] Tanenbaum, A. "Structured Computer Organization", Fourth Edition, Prentice
Hall, pages 631-640.
@#$#@#$#@
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NetLogo 2.0.1
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