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HWK 3

This document outlines Homework #3 for EECE 320 – Digital Systems Design, consisting of five problems focused on implementing digital functions using decoders and multiplexers. It includes tasks such as designing a high priority encoder, a 4-to-16 decoder, and a circuit to count the number of '0's in a 3-bit input. Each problem is assigned a point value, indicating its importance in the overall homework assignment.

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12 views2 pages

HWK 3

This document outlines Homework #3 for EECE 320 – Digital Systems Design, consisting of five problems focused on implementing digital functions using decoders and multiplexers. It includes tasks such as designing a high priority encoder, a 4-to-16 decoder, and a circuit to count the number of '0's in a 3-bit input. Each problem is assigned a point value, indicating its importance in the overall homework assignment.

Uploaded by

yareyaresass
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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EECE 320 – Digital Systems Design

Homework #3

Problem #1 [20 points]


Implement the following single-output or multi-output functions using the decoders
(74x138) and (74x139) with additional gates if need be.

a) 𝐹 = ∑𝐴,𝐵,𝐶(2,4,7)
b) 𝐹 = ∑𝐴,𝐵,𝐶,𝐷(2,3,4,5,8,10,12,14)
𝐹 = ∑𝐴,𝐵,𝐶(2,6)
c) {
𝐺 = ∑𝐶,𝐷,𝐸(0,2,3)

Problem #2 [20 points]


a) Implement the functions of Problem #1 (a & b) using an 8-input multiplexer.
b) Implement the functions of Problem #1 (a & b) using a 4-input multiplexer.

Problem #3 [20 points]


We want to design a high priority encoder that provides as an output the signals
corresponding to the highest TWO input signals. The circuit has 8 active low request signals
(I0, I1, …, I7) and 8 active high outputs: (A0, A1, A2) which indicate the value of the
highest input request, (B0, B1, B2) which indicate the value of the second highest input
request, (AVALID) which is activated if at least one input signal is active, and (BVALID)
which is activated to reflect that there is a second input request activated.
You can use all types of gates and as building blocks, you can use encoders and decoders.
Problem #4 [20 points]

Design a 4-to-16 decoder using the following components:

 One 3-to-8 decoder with one active-high enable bit.


 Three 2-to-4 decoders, each with one active-high enable bit.
 One 2-input OR gate.

You are not allowed to use inverters or any additional gates.

Problem #5 [20 points]

Design a circuit that counts the number of '0's in a given 3-bit input A (A2A1A0), and
produces a 2-bit output B (B1B0), representing the binary equivalent of the decimal count
of '0's in A. For example:

 A=111 results in B=00 (0 in decimal)


 A=101 results in B=01 (1 in decimal)
 A=100 results in B=10 (2 in decimal)
 A=000 results in B=11 (3 in decimal)

Draw the truth table and implement this function using one decoder, one encoder, and up
to two logic gates if necessary (inverters are not allowed).

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