Bit Representation LessonCS1313 Spring 2019
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Bit Representation Outline
Bit Representation OutlineHow Are Integers Represented in Memory?Decimal Number Representation (Base 10)Decimal (Base 10) BreakdownNonal Number Representation (Base 9)Nonal (Base 9) BreakdownOctal Number Representation (Base 8)Octal (Base 8) BreakdownTrinary Number Representation (Base 3)Trinary (Base 3) Breakdown
Binary Number Representation (Base 2)Binary (Base 2) Breakdown & ConversionCounting in Decimal (Base 10)Counting inNonal(Base 9)Counting in Octal (Base 8)Counting in Trinary (Base 3)Counting in Binary (Base 2)Counting in Binary (Base 2) w/Leading 0sCounting in Binary VideoAdding Integers #1Adding Integers #2Binary Representation ofintValues
Bit Representation LessonCS1313 Spring 2019
2
How Are Integers Represented in Memory?
In computers,alldata are represented ascontiguous sequences of bits.An integer is represented as a sequence of 8, 16, 32 or 64 bits. For example:What does this mean???
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97 =
Bit Representation LessonCS1313 Spring 2019
3
Decimal Number Representation (Base 10)
In thedecimalnumber system (base 10), we have10 digits:0 1 2 3 4 5 6 7 8 9We refer to these as theArabicdigits. For details, see:http://en.wikipedia.org/wiki/Arabic_numerals
Bit Representation LessonCS1313 Spring 2019
4
Decimal (Base 10) Breakdown
103
102
101
100
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7
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Jargon: 472110is pronounced “four seven two one base 10,” or “four seven two one decimal.”
Bit Representation LessonCS1313 Spring 2019
5
Nonal Number Representation (Base 9)
In thenonalnumber system (base 9), we have9 digits:0 1 2 3 4 5 6 7 8NOTE: No one usesnonalin real life; this is just an example.
Bit Representation LessonCS1313 Spring 2019
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Nonal (Base 9) Breakdown
93
92
91
90
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Jargon: 47219is pronounced “four seven two one base 9,” or “four seven two one nonal.”
=350210
So:47219=350210
Bit Representation LessonCS1313 Spring 2019
7
Octal Number Representation (Base 8)
In theoctalnumber system (base 8), we have8 digits:0 1 2 3 4 5 6 7NOTE: Some computer scientists used to use octal in real life, but it has mostly fallen out of favor, because it’s been supplanted by base 16 (hexadecimal).Octal does show up a little bit in C character strings., which we’ll learn about soon.
Bit Representation LessonCS1313 Spring 2019
8
Octal (Base 8) Breakdown
83
82
81
80
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1
Jargon: 47218is pronounced “four seven two one base 8,” or “four seven two one octal.”
=251310
So:47218=251310
Bit Representation LessonCS1313 Spring 2019
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Trinary Number Representation (Base 3)
In thetrinarynumber system (base 3), we have3 digits:0 1 2NOTE: No one uses trinary in real life; this is just an example.
Bit Representation LessonCS1313 Spring 2019
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Trinary (Base 3) Breakdown
33
32
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Jargon: 20213is pronounced “two zero two one base 3,” or “two zero two one trinary.”
= 6110
So:20213=6110
Bit Representation LessonCS1313 Spring 2019
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Binary Number Representation (Base 2)
In thebinarynumber system (base 2), we have2 digits:0 1This is the number system that computers use internally.
Bit Representation LessonCS1313 Spring 2019
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Binary (Base 2) Breakdown & Conversion
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9710=
Bit Representation LessonCS1313 Spring 2019
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Counting in Decimal (Base 10)
Inbase 10, wecountlike so:0,1, 2, 3, 4, 5, 6, 7, 8, 9, 10,11, 12, 13, 14, 15, 16, 17, 18, 19, 20,21, 22, 23, 24, 25, 26, 27, 28, 29, 30,...91, 92, 93, 94, 95, 96, 97, 98, 99, 100,101, 102, 103, 104, 105, 106, 107, 108, 109, 110,...191, 192, 193, 194, 195, 196, 197, 198, 199, 200,...991, 992, 993, 994, 995, 996, 997, 998, 999, 1000,...
Bit Representation LessonCS1313 Spring 2019
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Counting in Nonal (Base 9)
Inbase 9, wecountlike so:0,1, 2, 3, 4, 5, 6, 7, 8, 10,11, 12, 13, 14, 15, 16, 17, 18, 20,21, 22, 23, 24, 25, 26, 27, 28, 30,...81, 82, 83, 84, 85, 86, 87, 88, 100,101, 102, 103, 104, 105, 106, 107, 108, 110,...181, 182, 183, 184, 185, 186, 187, 188, 200,...881, 882, 883, 884, 885, 886, 887, 888, 1000,...
Bit Representation LessonCS1313 Spring 2019
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Counting in Octal (Base 8)
Inbase 8, wecountlike so:0,1, 2, 3, 4, 5, 6, 7, 10,11, 12, 13, 14, 15, 16, 17, 20,21, 22, 23, 24, 25, 26, 27, 30,...71, 72, 73, 74, 75, 76, 77, 100,101, 102, 103, 104, 105, 106, 107, 110,...171, 172, 173, 174, 175, 176, 177, 200,...771, 772, 773, 774, 775, 776, 777, 1000,...
Bit Representation LessonCS1313 Spring 2019
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Counting in Trinary (Base 3)
Inbase 3, wecountlike so:0,1, 2, 10,11, 12, 20,21, 22, 100,101, 102, 110,111, 112, 120,121, 122, 200,201, 202, 210,211, 212, 220,221, 222, 1000,...
Bit Representation LessonCS1313 Spring 2019
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Counting in Binary (Base 2)
Inbase 2, wecountlike so:0, 1,10, 11,100, 101, 110, 111,1000, 1001, 1010, 1011, 1100, 1101, 1110, 111110000, ...
Bit Representation LessonCS1313 Spring 2019
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Counting in Binary (Base 2) w/Leading 0s
Inbase 2, we sometimes like to put inleading zeros:00000000, 00000001,00000010, 00000011,00000100, 00000101, 00000110, 00000111,00001000, 00001001, 00001010, 00001011,00001100, 00001101, 00001110, 0000111100010000, ...
Counting in Binary Video
https://img-9gag-fun.9cache.com/photo/aq7Q4AZ_460svvp9.webm
Bit Representation LessonCS1313 Spring 2019
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Bit Representation LessonCS1313 Spring 2019
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Adding Integers #1
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9710=
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+ 1510=
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11210=
Bit Representation LessonCS1313 Spring 2019
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Adding Integers #2
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9710=
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+ 0610=
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10310=
Bit Representation LessonCS1313 Spring 2019
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Binary Representation ofintValues
%cat xadd.c#include <stdio.h>int main (){ /* main */int x;x = 97;printf("%d\n", x);x = x + 6;printf("%d\n", x);return 0;} /* main */%gcc -o xadd xadd.c%xadd97103
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