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# hw1sol - ECEN 248 Introduction to Digital System Design...

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ECEN 248: Introduction to Digital System Design Department of Electrical Engineering Texas A&M University Assignment #1 Solutions 1. Suppose I have a 3-variable function expressed as f = x 1 · x 2 + x 3 · x 1 . Write down The Canonical SOP expression for f The Canonical POS expression for f Solution. The function f consists of two cubes, c 1 = x 1 · x 2 and c 2 = x 3 · x 1 . Since these cubes have 2 literals each, and f has 3 variables, both these cubes contain 2 minterms each. The minterms of c 1 and c 2 are as follows: c 1 x 1 · x 2 · x 3 and x 1 · x 2 · x 3 . c 2 x 1 · x 2 · x 3 and x 1 · x 2 · x 3 In other words, c 1 = m 3 + m 7 . c 2 = m 1 + m 3 . Since f = c 1 + c 2 , CSOP ( f ) = m 1 + m 3 + m 7 From the above, we can write the CPOS of f as CPOS ( f ) = M 0 · M 2 · M 4 · M 5 · M 6 2. Consider a function which is expressed as f = x 1 · x 4 + x 3 · x 1 . Draw the truth table of f Solution. Note that the function depends on three variables x 4 , x 3 and x 1 . Therefore the truth table will have 3 inputs (and 2 3 = 8 rows). The truth table is shown in Figure 1.

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hw1sol - ECEN 248 Introduction to Digital System Design...

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