hw1 - a b c Hint Try to figure out how you can make NOT...

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[CSM51A W09] Assignment 1 Assigned: 01/12/09, Due: 01/19/09 TAs: Pouya Dormiani ([email protected]), Gabriel Pan ([email protected]) Rules of Engagement: Exercises are for your practice–solutions are provided so you can check your work. Homework problems must be submitted on the specified due date before lecture starts. Once lecture starts, a homework is considered late and will not be accepted. Please write legibly and follow directions. Exercises From the book: 2.27, 2.32, 2.42(b), 2.31, 2.47 Homework Problems (35 points total) Problem 1 (5 points) A multiplexor (MUX) is a 3-input function z ( x,y,s ) which outputs x when s = 1 and y when s = 0. Write the switching expression for a MUX then implement it using gates. S X Y Z 1 0 MUX Problem 2 (10 points) Convert the following sum of products (SOP) to a product of sums (POS) via algebraic manipulation using the identities of switching algebra. S ( a,b,c ) = ac 0 b + b 0 a + c 0 a 0 Problem 3 (10 points) Implement the following function using multiplexors. Draw the corresponding MUX network, S ( a,b,c ) = [ ab + (
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Unformatted text preview: a b + c ) ] ( Hint: Try to figure out how you can make NOT, AND and OR gates using MUXs. ) 1 Problem 4 (10 points) Your goal is to design a module which sums two digits x and y belonging to the set {-1 , , 1 } to produce an output in the set {-2 ,-1 , , 1 , 2 } . The inputs x and y are encoded via two bits, x p x n and y p y n with values given by x p-x n (i.e. setting x p = 0 and x n = 1 encodes -1, with zero having two possible encodings 00 and 11). The outputs are encoded via three bits z s ,z 1 ,z , whose value is interpreted via (-1) z s (2 z 1 + z ). 1. (2 points) Write the switching functions (in tabular form) to describe the system. 2. (2 points) Write the minterms (in m-notation) of z 1 and the maxterms (in M-notation) of z s . 3. (1 point) Do any of the switching functions have a dc-set? 4. (5 points) Implement z 1 via only AND and NOT gates ( Hint: figure out how to make an OR gate if you need one ). 2...
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hw1 - a b c Hint Try to figure out how you can make NOT...

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