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Binary and other number bases
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
Other number bases Bases two- Binary Base five- Quinary Base eight- Octal Base sixteen - Hexadecimal Bases are named for their “headings.”
Base Two Uses only 1’s and 0’s Headings are in powers of two 6432168421 1001100 Headings Binary number
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:
Base Eight Uses digits from 1 to 7 Headings are in powers of eights 6481 136 Headings Binary number
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:
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
Base Eight – converting to decimal 161 2B Headings Binary number = 32 + 11 = 43 Question: Convert 2B 16 to a decimal (base ten) number Answer:
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
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
Binary addition example 11 10110 +111 =11101 Carry’s Answer
Binary addition video https://www.youtube.com/watch?v=Cqs90dh w_E4 https://www.youtube.com/watch?v=Cqs90dh w_E4
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”
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
BCD exampl Convert 473 to binary coded decimal Answer: 4 7 3 =010001110011 We can separate the answer by spaces
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Try this! What number does BCD0101 1001 0001 represent? Answer: 010110010001 = 5 9 1 Answer: 591
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B AB CD C A D m0m1m3m2 m4 m5m7m6 m12 m8m9m11 m10 m13 m15m14 Input combo mintermExpressio n 0000m0A’B’C’D’ 0001m1A’B’C’D 0010m2A’B’CD’
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