# Problem Set 3

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**Due: Wednesday 26 October** before class.

In this problem set you'll get some practice working with gates and transistors. Please ask questions in class about any parts you don't understand.

## Problem 1. Mux Madness (40 points)

Suppose you wanted to implement a Boolean function Y of two inputs A and B using multiplexers, as shown in the figure.

Give binary values for I0, I1, I2, and I3 which implement the following functions on the two inputs A and B:

- Y = XOR(A,B)
- Y = (A == B)
- Y = (A <= B)
- Y = NOR(A,B)

## Problem 2. Go Forth and Multiply (30 points)

- Create a truth table showing multiplication of two 2-bit unsigned
integers A
_{1}A_{0}and B_{1}B_{0}, producing a 4-bit result P_{3}P_{2}P_{1}P_{0}. - Give the sum-of-products Boolean equation for each of the 4 outputs in the multiplier above.
- Assume that the 2-bit multiplier that you designed above is represented as the following function block:

Use this function block and single-bit full-adder blocks to build a 4-bit multiplier (a multiplier that takes two 4-bit inputs, and generates an 8-bit result). Note: Do not build the 4-bit multiplier from scratch using basic Boolean gates; you must build it using 2-bit multiplier blocks and full-adder blocks.

## Problem 3. Fishing for Complements (45 points)

Show the complementary set of p-channel or n-channel transistors that complete the following CMOS circuits, and give a truth table for the resulting circuit.