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 https://en.wikipedia.org/wiki/Pi https://en.wikipedia.org/wiki/To_be,_or_not_to_be

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!] https://en.wikipedia.org/wiki/Pi

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 https://en.wikipedia.org/wiki/To_be,_or_not_to_be

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 https://en.wikipedia.org/wiki/Numeral_system

Number Systems – Decimal Digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 Operations Addition ( 3 + 5 ) Subtraction ( 5 – 3 ) https://en.wikipedia.org/wiki/Decimal

Number Systems – Decimal Written Form Every “place” is 10 times the place to the right Number 1000 100 10 1 17 7 51 5 5281 2 8

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

Number Systems – Binary Digits 0, 1 Operations Addition ( 011 + 101 ) Subtraction ( 101 – 011 ) Fun new things (and, or, not, xor) https://en.wikipedia.org/wiki/Binary_number

Number Systems – Binary States can be easily represented in electronics Off False On True 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 51 5281

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

Familiar Numbers Decimal: 25 Binary: 11001 10 * 2 + 1 * 5 25 10000 + 01000 + 00001 11001 Number 1000 100 10 1 25 2 5 Number 128 64 32 16 8 4 2 1 11001

Converting to Binary Decimal 128 64 32 16 8 4 2 1 Binary 29 00011101 00011101 31 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 https://en.wikipedia.org/wiki/ASCII

ASCII □■□□□□□■ □■□□■■■■ □■□□□□■□ P 80 □■□■□□□□ □■□□□□■■ □■□■□□□■ 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 □□□■■■■■ 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

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? □■□■■□□□□■□■■□□■□■□■■□■□

Can You Write Your Initials? 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 ) 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 Program Storage 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 Turn left Turn right 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 Instructions Move forward Turn left Turn right etc. Instructions 11 01 10 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 Real Computer Programs 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 Instructions Load Add Jump Jump-if-equal Instructions 0001 0011 0101 0110

Complicated Programs Instructions Instructions Extra Load Add Jump Jump-if- equal Instructions 0001 0011 0101 0110 Extra What? Where? What/Where ?

Let’s Count to Ten Instructions Instructions Extra Load Add Jump Jump-if- equal Instructions 0001 0011 0101 0110 Extra 0000 0001 0101 1010

Let’s Count to Ten Instructions Instructions Extra 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 Instructions Extra 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 code code code code

Let’s Count to Ten Instructions Instructions Extra 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 Instructions Extra 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 Instructions Extra 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 Instructions Extra 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 code data code data code data data code data {