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Binary and other number bases

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Base Ten This is what we are accustomed to. Digits go from 0 – 9 Headings are represented by powers of ten ThousandsHundredsTensOnes= 4545 20792,079

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Other number bases Bases two- Binary Base five- Quinary Base eight- Octal Base sixteen - Hexadecimal Bases are named for their “headings.”

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Base Two Uses only 1’s and 0’s Headings are in powers of two 6432168421 1001100 Headings Binary number

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Base Two – converting to decimal 6432168421 1001100 Headings Binary number = 64 + 8 + 4 = 76 Question: Convert 1001100 2 to a decimal (base ten) number Answer:

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Base Eight Uses digits from 1 to 7 Headings are in powers of eights 6481 136 Headings Binary number

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Base Eight – converting to decimal 6481 136 Headings Binary number = 64 + 24 + 6 = 94 Question: Convert 136 8 to a decimal (base ten) number Answer:

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Base Sixteen Uses digits from 1 to 9, and letters from A to F (10 to 15) Headings are in powers of 16’s 161 2B Headings Binary number

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Base Eight – converting to decimal 161 2B Headings Binary number = 32 + 11 = 43 Question: Convert 2B 16 to a decimal (base ten) number Answer:

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Review: Binary to Decimal https://www.youtube.com/watch?v=UUqtjb8 WEUs https://www.youtube.com/watch?v=UUqtjb8 WEUs New: Converting a decimal to binary https://www.youtube.com/watch?v=qWxiXU0 2ZQM https://www.youtube.com/watch?v=qWxiXU0 2ZQM

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Binary addition Basic rules 1 0 1 0 1 1 +0+ 0 + 1 =0 1 11 01 0 and carry 1 1 and carry 1

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Binary addition example 11 10110 +111 =11101 Carry’s Answer

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Binary addition video https://www.youtube.com/watch?v=Cqs90dh w_E4 https://www.youtube.com/watch?v=Cqs90dh w_E4

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Other binary BCD – Binary Coded Decimal Every digit of a number is represented using its 4-bit binary equivalent The number is not “converted,” instead each digit is given a “code”

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0=0000 1=0001 2=0010 3=0011 4=0100 5=0101 6=0110 7=0111 8=1000 9=1001 A negative sign is represented by 1011

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BCD exampl Convert 473 to binary coded decimal Answer: 4 7 3 =010001110011 We can separate the answer by spaces

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BCD example 2 Convert -93 to SIGNED BCD Answer: - 9 3 =111110010011

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Try this! What number does BCD0101 1001 0001 represent? Answer: 010110010001 = 5 9 1 Answer: 591

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