Digital Logic HW 1 solutions

Digital Logic HW 1 solutions - Homework 1 Solution. Problem...

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Homework 1 Solution. Problem 1 Determine if the following expression is valid by using a truth table and by using algebraic manipulation: ( ) ( ) ( ) 3 2 1 3 2 1 3 2 1 3 2 3 2 3 1 x x x x x x x x x x x x x x x + + + + + + = + + Solving LHS by expanding the product terms into minterms. ( ) ( ) ( ) 3 2 1 3 2 1 3 2 1 3 2 1 3 2 1 3 2 1 3 2 1 1 3 2 1 1 3 2 2 1 3 2 3 2 3 1 x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x + + + + + = + + + + + = + + Solving the RHS by multiplying the sum terms to express the function in the sum of products form. ( ) ( ) ( ) () () () () () () () () () () () () () () () () () () 3 2 1 3 2 1 3 2 1 3 2 1 3 2 1 3 2 1 3 2 1 3 2 1 3 2 1 3 2 1 3 2 1 3 2 1 3 2 1 3 2 1 3 2 1 3 2 1 3 2 1 3 2 1 3 2 1 3 2 1 3 2 1 3 2 1 3 2 1 1 3 2 1 3 2 1 3 2 1 3 2 1 3 2 1 3 2 2 1 3 3 2 1 3 2 1 3 2 1 3 2 1 3 2 3 2 1 3 2 1 3 2 1 3 2 1 3 2 1 3 1 2 1 3 2 1 3 2 1 3 2 1 2 3 2 3 1 2 3 1 3 2 1 3 1 3 2 3 1 2 2 3 1 3 2 1 2 1 3 1 2 1 3 2 1 3 2 1 3 2 1 3 3 3 2
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Digital Logic HW 1 solutions - Homework 1 Solution. Problem...

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