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09_Arithmetic

# 09_Arithmetic - William Stallings Computer Organization and...

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William Stallings Computer Organization and Architecture 7 th Edition Chapter 9 Computer Arithmetic

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Arithmetic & Logic Unit Does the calculations Everything else in the computer is there to  service this unit Handles integers May handle floating point (real) numbers May be separate FPU (maths co-processor) May be on chip separate FPU (486DX +)
ALU Inputs and Outputs

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Integer Representation Only have 0 & 1 to represent everything Positive numbers stored in binary e.g. 41=00101001 No minus sign No period Sign-Magnitude Two’s compliment
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)

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Two’s Compliment +3 = 00000011 +2 = 00000010 +1 = 00000001 +0 = 00000000  -1 = 11111111  -2 = 11111110  -3 = 11111101
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

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Geometric Depiction of Twos Complement Integers
Negation Special Case 1  0 =                00000000 Bitwise not       11111111 Add 1 to LSB              +1 Result           1 00000000 Overflow is ignored, so: - 0 = 0

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09_Arithmetic - William Stallings Computer Organization and...

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