number_representation

# number_representation - Integer Representation

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Integer Representation Positive numbers stored in binary e.g. 41=00101001 No minus sign No period Sign-Magnitude Two’s compliment

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Sign-Magnitude Left most bit is sign bit 0 means positive 1 means negative +18 = 00010010  -18 = 10010010 Problems Need to consider both sign and magnitude in  arithmetic Two representations of zero (+0 and -0)
Two’s Compliment +3 = 00000011 +2 = 00000010 +1 = 00000001 +0 = 00000000  -1 = 11111111  -2 = 11111110  -3 = 11111101

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Benefits One representation of zero Arithmetic works easily (see later) Negating is fairly easy 3 = 00000011 Boolean complement gives 11111100 Add 1 to LSB 11111101
Geometric Depiction of Twos Complement Integers

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Negation Special Case 1  0 =                00000000 Bitwise not       11111111 Add 1 to LSB              +1 Result           1 00000000 Overflow is ignored, so: - 0 = 0
Negation Special Case 2 -128 =           10000000 bitwise not     01111111

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## This note was uploaded on 04/20/2010 for the course CS 102 taught by Professor Kp during the Spring '10 term at Jaypee University IT.

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number_representation - Integer Representation

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