CPRE281_HW08_SOLUTION

# CPRE281_HW08_SOLUTION - Cpr E 281 HW08 SOLUTION ELECTRICAL...

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Cpr E 281 HW08 SOLUTION ELECTRICAL AND COMPUTER ENGINEERING IOWA STATE UNIVERSITY Arithmetic Circuits and Combinational-Circuit Building blocks Assigned Date: Eighth Week Due Date: Mar. 23, 2016, 9.00 AM 1 P1. (10 points) Consider constructing a 2 n x1 multiplexer using only 2x1 multiplexers, with n being a positive integer. (a) How many 2x1 multiplexers would a 2 n x1 multiplexer require? Give an answer in terms of n.

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Cpr E 281 HW08 SOLUTION ELECTRICAL AND COMPUTER ENGINEERING IOWA STATE UNIVERSITY Arithmetic Circuits and Combinational-Circuit Building blocks Assigned Date: Eighth Week Due Date: Mar. 23, 2016, 9.00 AM 2 (b) Design an 8x1 multiplexer (8=2 3 ) using a minimal number of 2x1 multiplexers. Please label all signals clearly.
Cpr E 281 HW08 SOLUTION ELECTRICAL AND COMPUTER ENGINEERING IOWA STATE UNIVERSITY Arithmetic Circuits and Combinational-Circuit Building blocks Assigned Date: Eighth Week Due Date: Mar. 23, 2016, 9.00 AM 3 P2. (10 points) Consider a function F with 4 bits of input A 3 ,A 2 ,A 1 ,A 0 such that the output of F is 1 if the unsigned binary number represented by A 3 A 2 A 1 A 0 is integer divisible by 3 or 7 (i.e., 0, 3, 6, 7, 9, 12, 14 or 15). Otherwise, the output of F is 0. (a) Write the truth table for F. (b) Implement F using ONE 16x1 MUX and nothing else. A3 A2 A1 A0 F 0 0 0 0 1 A0’ 0 0 0 1 0 0 0 1 0 0 A0 0 0 1 1 1 0 1 0 0 0 0 0 1 0 1 0 0 1 1 0 1 1 0 1 1 1 1 1 0 0 0 0 A0 1 0 0 1 1 1 0 1 0 0 0 1 0 1 1 0 1 1 0 0 1 A0 1 1 0 1 0 1 1 1 0 1 1 1 1 1 1 1

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Cpr E 281 HW08 SOLUTION ELECTRICAL AND COMPUTER ENGINEERING IOWA STATE UNIVERSITY Arithmetic Circuits and Combinational-Circuit Building blocks Assigned Date: Eighth Week Due Date: Mar. 23, 2016, 9.00 AM 4 (c) Use A 3 A 2 A 1 as select variables. Use the truth table in part(a) to implement F using an 8x1 MUX, some AND gates, some OR gates, and some NOT gates if necessary. (d) Use A 3 ,A 2 ,A 1 ,A 0 as select variables in that order. Implement F using ONLY 2x1 Multiplexers from the truth table in part(a).
Cpr E 281 HW08 SOLUTION ELECTRICAL AND COMPUTER ENGINEERING IOWA STATE UNIVERSITY Arithmetic Circuits and Combinational-Circuit Building blocks Assigned Date: Eighth Week Due Date: Mar. 23, 2016, 9.00 AM 5 P3. (15 points) Use Shannon’s Expansion

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