Homework 2

Due: Saturday, July 20 at 11:59PM

Submission: On Courseworks

Instructions

Complete the following assignment and submit on courseworks in either doc, docx, or pdf format. If you complete the assignment on pen/paper, please create a word or pdf document using clear images or scans of your physical copy.

1. Mux Puzzle

Implement an OR gate using only a two-input mux and constant inputs (in addition to inputs A and B)

2. Game Circuit

We construct the following circuit representing a game. Our circuit has the following inputs:

• P0 - player zero’s choice
• P1 - player one’s choice
• C - player zero’s choice of “not matching” or “matching”

For C==1, the output (called f) is 1 if P0 and P1 are equal (P0 == P1 == 1 or P0 == P1 == 0), and 0 if not (P0 != P1). For C==0, the output is 1 if P0 and P1 are not equal and 0 if they are (e.g. the reverse behavior of C==1).

Implement the following:

• a truth table for the output
• the minterm representation
• the maxterm representation
• a minimal representation using Karnaugh maps

3. Combinational Logic

Show how to implement

f = X̅ Y̅ Z + Y Z̅ + X Y̅

using:

• a 3-to-8 decoder and an OR gate
• an 8 input mux
• a 4 input mux whose select inputs are X and Y and an inverter

4. Combinational Logic

Draw a circuit for an eight input mux using three four-input muxes and no other gates.

5. Combinational Logic

Consider the following circuit:

Under what conditions could the output of this circuit glitch high? I.e. for what assignment of input values would changing one input’s value cause the output to briefly transition from 0 to 1 to 0? Modify the circuit (add or change gates and wires) so it computes the same function but cannot glitch in this situation.

6. Combinational Logic

Implement a three-bit binary carry-lookahead adder. Its inputs are A0,…,A2 and B0,…,B2 for the two addends, and C0 for the carry in. Its outputs are Y0,…,Y3

• Write expressions for G0,…,G2 and P0,…,P2, the carry generate and propogate functions, in terms of the inputs.
• Write sum-of-product expressions for C1,…,C3 in terms of the G’s, P’s, and C0
• Use these to write equations for the Y’s (use “⊕” for XOR)
• Draw the carry-lookahead adder circuit corresponding to these equations using inverters, AND, NAND, OR, NOR, and XOR gates with as many inputs as you’d like. The critical path should be four gates. Please be neat.