L6 ALU - Computer Science 230H ALU Computer Arithmetic...

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Computer Science 230H ALU – Computer Arithmetic Prepared by Michael Jack Fall 2007 Slides set 2
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ALU 2 References The information and figures for the following slides were prepared from the following source: Patterson, D., and Hennessy J., Computer Organization and Design, 3rd edition, 2005 Stallings, W., Computer Organization and Architecture: Designing for Performance 7 th edition, 2006 Hircock B., Computer Science 230 Course Notes
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ALU 3 Compared with addition and subtraction, multiplication is a complex operation. – Performed in hardware and software. A number of methods exist to perform unsigned integer multiplication: Repeated addition - add the multiplicand to itself “multiplier” times. Shift and add - traditional “pen and paper” way of multiplying (extended to binary format.) High speed (special purpose) hardware multipliers. Integer Multiplication
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4 Repeated addition – Least sophisticated method. – Just use adder over and over again. – If the multiplier is n bits, can have as many as 2n iterations of addition - O(2n)! – Not used in ALU Unsigned Integer Multiplication Shift and add – Computer’s version of the “pen and paper” approach: – The algorithm accumulates the partial products into a running (partial) sum as it progresses – Each partial product generation results in an add and shift operation – When the multiplier bit is 0, the partial product is 0; when it is 1, the partial product is 1. – The final product is up to 2
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L6 ALU - Computer Science 230H ALU Computer Arithmetic...

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