Examine multiplier bits in groups of 2s plus a helper bit on the right (as opposed to 1 bit plus helper bit on right). ⢠Means we'll need to shift product/multiplier by 2 ...
Booth In Action • For each multiplier bit, also examine bit to its right • • • •
00: 10: 11: 01:
* + + +
middle of a run of 0s, do nothing beginning of a run of 1s, subtract multiplicand middle of a run of 1s, do nothing end of a run of 1s, add multiplicand
Booth in Summary • Performance/efficiency + Good for sequences of 3 or more 1s • Replaces 3 (or more) adds with 1 add and 1 subtract • Doesn’t matter for sequences of 2 1s • Replaces 2 adds with 1 add and 1 subtract (add = subtract) – Actually bad for singleton 1s • Replaces 1 add with 1 add and 1 subtract
• Bottom line • Worst case multiplier (101010) requires N/2 adds + N/2 subs • What is the worst case multiplier for straight multiplication? • How is this better than normal multiplication?
Modified Booth’s Algorithm • What if we detect singleton 1s and do the right thing? • Examine multiplier bits in groups of 2s plus a helper bit on the right (as opposed to 1 bit plus helper bit on right) • Means we’ll need to shift product/multiplier by 2 (not 1) • 000: middle of run of 0s, do nothing • 100: beginning of run of 1s, subtract multiplicand
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