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PS3-solutions-fall09

PS3-solutions-fall09 - COMS W1004 Fall 2009 Problem Set 3...

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COMS W1004 Fall 2009 Problem Set 3 Chapter 4 17. 5pts (they need to follow circuit construction algorithm giving step by step process on obtaining the circuit) The circuit corresponds to : They can also write an optimized version of the above equations as follows: (correspondingly the circuit should be drawn in such case) or 19. 5pts (should explain steps as well) The circuit corresponds to [(b.c)+(a.c)+(a.b)+(a.b.c)].
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The circuit can be constructed as in previous problem, it would contain AND gates for (.) Product and OR gates for the (+) summation. 21. 5pts (Should explain the steps also) So the sum of products expressions for a b and Next Borrow are a b = Next Borrow = The circuit may be constructed as in the previous problems. Challenge Work 1 5pts Changes may really only be made to the 1-bit adder. However a small change in the 1-bit adder will multiply to a larger effect in the overall circuit. An easy first step is to have both the s i and c i -1 outputs share the portion of the circuits that computes a * b * c. There is no other reason to have two copies of that sub-circuit. That alone will save two AND gates per 1-bit adder. For a 32-bit adder, it will save 64 x 2 transistors.
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