lec20-arith1.pdf - EECS150 Digital Design Lecture 20 – Arithmetic Blocks 1 Elad Alon Electrical Engineering and Computer Sciences University of

# lec20-arith1.pdf - EECS150 Digital Design Lecture 20 –...

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Fall 2011 EECS150 Lecture 19 Page 1 EECS150 - Digital Design Lecture 20 – Arithmetic Blocks 1 November 10, 2011 Elad Alon Electrical Engineering and Computer Sciences University of California, Berkeley Fall 2011 EECS150 Lecture 19 Page 2 Announcements Project checkpoint #4a due this Fri., #4b due next Fri. Be sure to check off even if you aren’t totally finished in order to receive partial credit The more tests you’ve written, the more credit you will get (Even if you don’t pass all of the tests) No more homeworks Will post an “optional” homework #8 to help you study for the final
Fall 2011 EECS150 Lecture 19 Page 3 Arithmetic Block Design Fall 2011 EECS150 Lecture 19 Page 4 Carry-ripple Adder Revisited Each cell: r i = a i XOR b i XOR c in c out = a i c in + a i b i + b i c in = c in (a i + b i ) + a i b i 4-bit adder: What about subtraction? “Full adder cell”
Fall 2011 EECS150 Lecture 19 Page 5 Subtractor A - B = A + (-B) How do we form -B? 1. complement B 2. add 1 Fall 2011 EECS150 Lecture 19 Page 6 Delay in Ripple Adders Ripple delay amount is a function of the data inputs: What is the critical path? 1 0 0 1 0 1 1 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0 0 1 1 0 1 0 1 1 1 0 0 0 1 1 t 0 t 1 t 2 t 3