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# ps3 - Massachusetts Institute of Technology Department of...

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Massachusetts Institute of Technology Department of Aeronautics and Astronautics 16.682 – Special Subjects in Aeronautics and Astronautics “Prototyping Avionics” Homework #3 Out: Wed Mar 8, 2006 Due: Wed Mar 15, 2006 Topics: Digital Logic elements Basic Logic Multiplexers Latches, Flip-Flops, & Registers “Thinking Digital” Notation and bases Bitwise vs. Wordwise Shifting Data types, 2’s complement Problem 1 – Basic Logic First, lets make sure that you have a quick feeling for how the basic two-input logic gates work. Using 2-input AND, NAND, OR, and NOR gates make: 1) a 2-input XOR gate Using only 2-input logic gates (AND, NAND, OR, NOR, or XOR) make: 1) a 5-input AND gate 2) a 5-input OR gate Show the truth-tables for both gates with as few rows as possible. (tip: try to use a lot of “don’t care” x’s) The idea to take with you is to see how: a) Complex circuits are a lot of simple ones put together b) To make complex design you start to use a lot of logic gates (many transistors) 16.682 “Prototyping Avionics” 1/8 Problem Set 3 SP06

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Problem 2 – Multiplexers In class we saw a 2-input and a 4-input multiplexer. Now it is your turn to show how a 6-input multiplexer would look like: 1) How may “select” control lines are needed? 2) Draw the symbol for a six input multiplexer – a single symbol, do not use many multiplexers to create this one. 3) Show the truth table as simple as possible… do you have extra rows? 4) What is the number of inputs needed to use all select lines? 5) What if you used a 2-input and 4-input multiplexer, and then combined the signal, would you use all the select lines? Problem 3 – Latches, Flip-Flops, and Registers 1) Latches The most simple latch out there is one that only has only three connections: set, reset, output: S Q R The signal Q goes high when Set is asserted, and it goes low when R is asserted. a) Draw the truth table for this latch --- point out any states you’re not sure about b) Create this latch by using the latch we saw in class (inputs: D, S, R; output: Q) and connecting the input signals as needed. The diagram below illustrates this question. (Tip: don’t over think it, this part should take 10 seconds, the answer is extremely simple!) S R Q S R Q D 16.682 “Prototyping Avionics” 2/8 Problem Set 3 SP06
Lets re-visit the timing problem with latches.

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ps3 - Massachusetts Institute of Technology Department of...

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