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Introduction to Binary
Why Bother with Binary?
● This is all about electronics● We don’t use binary because electronics do● We designed electronics to use binary
because it is very easy to do so● Trying to use decimal inside electronics would
be crazy difficult
Why Bother with Binary?
● Operations are easy in electronics (just wait!)● Binary numbers can be used to represent
anything
Why Bother with Binary?
● Operations are easy in electronics (just wait!)● Binary numbers can be used to represent
anything– Numbers!
Why Bother with Binary?
● Operations are easy in electronics (just wait!)● Binary numbers can be used to represent
anything– Numbers! π = 3.1415926535 [and more!]
Why Bother with Binary?
● Operations are easy in electronics (just wait!)● Binary numbers can be used to represent
anything– Numbers! π = 3.1415926535 [and more!]– Words “To be, or not to be!”– Pictures – Videos
Why Bother with Binary?
● Operations are easy in electronics (just wait!)● Binary numbers can be used to represent
anything– Numbers! π = 3.1415926535 [and more!]– Words “To be, or not to be!”– Pictures – Videos– Programs (like games!)
Number Systems
● Ways to organize and write numbers● Set of digits● Set of operations
– Addition– Subtraction
Number Systems – Decimal
● Digits– 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
● Operations– Addition ( 3 + 5 )– Subtraction ( 5 – 3 )
Number Systems – Decimal
● Written Form● Every “place” is 10 times the place to the right
Number 1000 100 10 1
17 0 0 1 7
51 0 0 5 1
5281 5 2 8 1
Number Systems – Decimal
● What’s going on, here?
1000 * 5
+ 100 * 2
+ 10 * 8
+ 1 * 1
= 5281
Number 1000 100 10 1
5281 5 2 8 1
Number Systems – Binary
● Digits– 0, 1
● Operations– Addition ( 011 + 101 )– Subtraction ( 101 – 011 )– Fun new things (and, or, not, xor)
Number Systems – Binary
States can be easily represented in electronics
OffFalse0
OnTrue
1
Number System - Binary
● Written Form● Every “place” is twice the place to the right
Number 4096 2048 1024 512 256 128 64 32 16 8 4 2 1
17 0 0 0 0 0 0 0 0 1 0 0 0 1
51 0 0 0 0 0 0 0 1 1 0 0 1 1
5281 1 0 1 0 0 1 0 1 0 0 0 0 1
Number Systems – Binary
● Same number as before
1000000000000
+ 0010000000000
+ 0000010000000
+ 0000000100000
+ 0000000000001
= 1010010100001
Number 4096 2048 1024 512 256 128 64 32 16 8 4 2 1
5280 1 0 1 0 0 1 0 1 0 0 0 0 1
Familiar Numbers
● Decimal: 25 10 * 2
+ 1 * 5
25
● Binary: 11001 10000
+ 01000
+ 00001
11001
Number 128 64 32 16 8 4 2 1
11001 0 0 0 1 1 0 0 1
Number 1000 100 10 1
25 0 0 2 5
Converting to Binary
Decimal 128 64 32 16 8 4 2 1 Binary
29 0 0 0 1 1 1 0 1 00011101
31
32
33
100
111
125
Binary Numbers
● Just another way to “write” the numbers you see every day
Numbers with Meaning
● How do we represent words in computers?
Numbers with Meaning
● How do we represent words in computers?
Numbers!
Numbers with Meaning
● How do we represent words in computers?
Numbers!
(Bet you didn’t see what one coming...)
ASCII
● American Standard Code for Information Interchange
● A special set of numbers to represent letters● All letters have a number assigned to them
ASCII
Letter Decimal Binary Pattern
A 65 01000001 □■□□□□□□■B 66 01000010 □■□□□□□□■C 67 01000011 □■□□□□□□■D 68 01000100 □■□□□□□□■E 69 01000101
F 70 01000110
G 71 01000111
H 72 01001000
I 73 01001001
J 74 01001010
K 75 01001011
L 76 01001100
M 77 01001101
N 78 01001110
O 79 01001111
Letter Decimal Binary Pattern Letter Decimal Binary Pattern
A 65 01000001 □■□□□□□■ O 79 01001111 □■□□■■■■B 66 01000010 □■□□□□■□ P 80 01010000 □■□■□□□□C 67 01000011 □■□□□□■■ Q 81 01010001 □■□■□□□■D 68 01000100 □■□□□■□□ R 82 01010010 □■□■□□■□E 69 01000101 □■□□□■□■ S 83 01010011 □■□■□□■■F 70 01000110 □■□□□■■□ T 84 01010100 □■□■□■□□G 71 01000111 □■□□□■■■ U 85 01010101 □■□■□■□■H 72 01001000 □■□□■□□□ V 86 01010110 □■□■□■■□I 73 01001001 □■□□■□□■ W 87 01010111 □■□■□■■■J 74 01001010 □■□□■□■□ X 88 01011000 □■□■■□□□K 75 01001011 □■□□■□■■ Y 89 01011001 □■□■■□□■
L 76 01001100 □■□□■■□□ Z 90 01011010 □■□■■□■□M 77 01001101 □■□□■■□■ ! 33 00100001 □□■□□□□■N 78 01001110 □■□□■■■□ ? 63 00011111 □□□■■■■■
Making Words From Letters
● How do we write our ABCs?
Making Words From Letters
● How do we write our ABCs?● Like this:
□■□□□□□■□■□□□□■□□■□□□□■■
Making Words From Letters
● How do we write our ABCs?● Like this:
□■□□□□□■□■□□□□■□□■□□□□■■ ● How about XYZ?
Making Words From Letters
● How do we write our ABCs?● Like this:
□■□□□□□■□■□□□□■□□■□□□□■■ ● How about XYZ?● Like this:
□■□■■□□□□■□■■□□■□■□■■□■□
Can You Write Your Initials?
Letter Decimal Binary Pattern Letter Decimal Binary Pattern
A 65 01000001 □■□□□□□■ O 79 01001111 □■□□■■■■B 66 01000010 □■□□□□■□ P 80 01010000 □■□■□□□□C 67 01000011 □■□□□□■■ Q 81 01010001 □■□■□□□■D 68 01000100 □■□□□■□□ R 82 01010010 □■□■□□■□E 69 01000101 □■□□□■□■ S 83 01010011 □■□■□□■■F 70 01000110 □■□□□■■□ T 84 01010100 □■□■□■□□G 71 01000111 □■□□□■■■ U 85 01010101 □■□■□■□■H 72 01001000 □■□□■□□□ V 86 01010110 □■□■□■■□I 73 01001001 □■□□■□□■ W 87 01010111 □■□■□■■■J 74 01001010 □■□□■□■□ X 88 01011000 □■□■■□□□K 75 01001011 □■□□■□■■ Y 89 01011001 □■□■■□□■L 76 01001100 □■□□■■□□ Z 90 01011010 □■□■■□■□M 77 01001101 □■□□■■□■ ! 33 00100001 □□■□□□□■N 78 01001110 □■□□■■■□ ? 63 00011111 □□□■■■■■
Bonus
● Can you decode the binary code on my shirt?
Arithmetic in Binary
● Easy– You only need to know how to add 0 and 1
● Hardest operation you ever have to do is 1 + 1– Hint: the answer isn’t “2”
Addition – Decimal
● 2 + 2 =● 2 + 8 =● 7 + 8 =
Addition – Binary
● 0 + 0 =● 0 + 1 =● 1 + 0 =● 1 + 1 =
Addition – Binary
● 10 + 10 = ( 2 + 2 )● 10 + 1000 = ( 2 + 8 )● 111 + 1000 = ( 7 + 8 )● 10110 + 01011 = ( 22 + 11 )
Funny Operators
● And– 0 0 = 0∧
– 0 1 = 0∧
– 1 0 = 0∧
– 1 1 = 1∧
● Or–
Programs in Binary
● Everything in a computer is represented with binary numbers
● Programs in a computer are (of course!) represented in binary numbers
Programs in Binary
● Instructions– List of things you can do
● Program– List of instructions, in order
● Storage– Instructions, encoded into binary, in the computer’s
memory
Programs in Binary - Instructions
● Human Robots– Just like our first week in Coding Club– Can move forward– Can turn right– Can turn left
Programs in Binary
● Program– Move forward– Move forward– Turn left– Move forward– Turn right– Move forward– etc.
Programs in Binary
● Instructions .. in binary!– We have 3 instructions– We will need two “bits” for each instruction– 2 bits can represent 0, 1, 2, or 3 in decimal– We only need 3 of these 4; one of them will be
unused
Programs in Binary
● Instructions .. in binary!– Turn left: 01– Turn right: 10– Move forward: 11
Programs in Binary
● Program– Move forward– Move forward– Turn left– Move forward– Turn right– Move forward– etc.
● Instructions– 11– 11– 01– 11– 10– 11– etc.
Programs in Binary
● Program in computer memory– 111101111011
or– ■■■■□■■■■□■■
How Does a Computer Run a Program?
● Program is in memory– ■■■■□■■■■□■■
● Computer knows all instructions are 2-bits wide● Computer starts at the beginning
– Read 2 bits– Decide which instruction is represented– Perform instruction (e.g. turn, move)– Repeat
Complicated Programs
● Human Robots– Limited to turn, move
● Real Computer Programs– Can do much more
Complicated Programs
● Perform arithmetic● Make decisions● Run loops● Load/store information
Complicated Programs
● Require lots of instructions● Examples:
– load, store– add, subtract– compare– jump!
Complicated Programs
● Instructions– Load– Add– Jump– Jump-if-equal
● Instructions– 0001– 0011– 0101– 0110
Complicated Programs
● Instructions– Load– Add– Jump– Jump-if-
equal
● Instructions– 0001– 0011– 0101– 0110
● Extra– What?– What?– Where?– What/Where
?
Let’s Count to Ten
● Instructions– Load– Add– Jump– Jump-if-
equal
● Instructions– 0001– 0011– 0101– 0110
● Extra– 0000– 0001– 0101– 1010
Let’s Count to Ten
● Instructions– Load– Add– Jump– Jump-if-
equal
● Instructions– 0001– 0011– 0101– 0110
● Extra– 0000– 0001– 0101– 1010
0001 0000 0011 0001 0110 1010 0101 0101 0101
Let’s Count to Ten
● Instructions– Load– Add– Jump– Jump-if-
equal
● Instructions– 0001– 0011– 0101– 0110
● Extra– 0000– 0001– 0101– 1010
0001 0000 0011 0001 0110 1010 0101 0101 0101code code code code
Let’s Count to Ten
● Instructions– Load– Add– Jump– Jump-if-
equal
● Instructions– 0001– 0011– 0101– 0110
● Extra– 0000– 0001– 0101– 1010
0001 0000 0011 0001 0110 1010 0101 0101 0101 data data data data data
Complicated Programs
● Instructions– Load– Add– Jump– Jump-if-
equal
● Instructions– 0001– 0011– 0101– 0110
● Extra– 0000– 0001– 0101– 1010
0001 0000 0011 0001 0110 1010 0101 0101 0101 data data data data data
?
Complicated Programs
● Instructions– Load– Add– Jump– Jump-if-
equal
● Instructions– 0001– 0011– 0101– 0110
● Extra– 0000– 0001– 0101– 1010
0001 0000 0011 0001 0110 1010 0101 0101 0101 data data data data data
}
Complicated Programs
● Instructions– Load– Add– Jump– Jump-if-
equal
● Instructions– 0001– 0011– 0101– 0110
● Extra– 0000– 0001– 0101– 1010
0001 0000 0011 0001 0110 1010 0101 0101 0101code data code data code data data code data
}
{