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let5-Adders and Multipliers

# Computer Arithmetic: Algorithms and Hardware Designs

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CSE 246: Computer Arithmetic Algorithms and Hardware Design Instructor: Prof. Chung-Kuan Cheng Fall 2006 Lecture 5: Addition and Multiplication

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CSE 246 2 Topics: False Path: Cycles Multi-Operands Addition Carry Save Addition Multiplication 2’s Complement Booth Recoding
CSE 246 3 False Path: Cycles Cycles of False Paths: Eg. 1’s complement number addition Positive: x Negative: (2 n -1)-x Addition (2 n -1)-x + (2 n -1)-y = 2 n +(2 n -1)-(x+y)-1 C out A 3,0 B 3,0 S 3,0 Adder C in

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CSE 246 4 Example -3-5 = -8 11100 -3 + 11010 -5 110110 110111 -8 0+0=0 11111 0 + 11111 0 111110 111111 0
CSE 246 5 Multi-Operand Addition Carry save adder: a (3,2) counter

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CSE 246 6 Example A (3,2) counter compresses X rows to 2/3X rows each time Tree structure in implementation A G H D C B F E A E C B F H G D
CSE 246 7 Other Counters (5,3) counter C a C b S 0 (7,3) counter 7 S 0 S 2 S 1 Design of (5,3) counter using full adders FA FA C a C b S 0

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CSE 246 8 Multiplication Examples 0101 5 * 0110 6 0000 0101 0101 0000 0011110 30 0101 5 * 1010 -6 0000 0101 0101 1011 1100010 -30 2’s complement of -5
CSE 246 9 Multiplication Examples (Cont.)

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