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SOEN228_11w_week9supp - SOEN229 11w Week 9 supplemental...

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SOEN229 11w Week 9 supplemental NASM arithmetic
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Data Representation Numbering Systems Decimal System the number 123 represents: 1*10 2 + 2*10 1 + 3*10 0 or 100+20+3 The Binary Numbering System the binary value 11001010 2 represents: 1*2 7 + 1*2 6 + 0*2 5 + 0*2 4 + 1*2 3 +
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Conversions convert decimal to binary Successive division by 2, build the binary by concatenating the remainders 202/2 = 101, remainder is 0 2 0 101/2=50, remainder is 1 2 1 50/2=25 remainder is 0 2 2 25/2=12 remainder is 1 2 3 12/2=6 remainder is 0 2 4 6/2=3 remainder is 0 2 5 3/2=1 remainder is 1 2 6 1/2 =0 remainder is 1 2 7 Result = 1100101
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Hexadecimal Shorthand notation for binary, 4 bits at a time 11001010 can be represented as 1100 1010 = CAh Note that 4 bits give 16 combinations, from 0 to 15. In Hex, we refer to 10 as A, 11 as B, etc. 1010 = 10 in decimal = A in hex 1011 = 11 in decimal = B in hex 1100 = 12 in decimal = C in hex 1101 = 13 in decimal = D in hex 1110 = 14 in decimal = E in hex 1111 = 15 in decimal = F in hex
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Conversion to decimal Binary to decimal Multiplication by successive powers of 2 11001010 1*2 7 + 1*2 6 + 0*2 5 + 0*2 4 + 1*2 3 + 0*2 2 + 1*2 1 + 0*2 0 » = 128 + 64 + 8 + 2 » = 202 10 (as in previous slide) Hex to decimal Multiplication by successive powers of 16. For example, the number 1234 16 is equal to: » 1 * 16 3 + 2 * 16 2 + 3 * 16 1 + 4 * 16 0 » or » 4096 + 512 + 48 + 4 = 4660 10 .
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Unsigned and signed integers in binary Unsigned integers are all positive numbers
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