This document contains 4 questions related to Boolean algebra expressions: 1) Determine if 3 Boolean expressions are valid by checking if they represent the same function. 2) Find the minimum sum-of-products expression for a given Boolean function. 3) Draw the waveform of a Boolean function given the waveforms of its inputs. 4) Find the minimum product-of-sums expression for a given Boolean function.

1. 1) [15%] Determine whether or not the following expressions are valid, i.e., whether the left-
hand and right-hand sides represent the same function. (a) x 1 x 3 + x 1 x 2 x 3 + x 1 x 2 + x 1 x
2 = x 2 x 3 + x 1 x 3 + x 2 x 3 + x 1 x 2 x 3 (b) x 1 x 3 + x 2 x 3 + x 2 x 3 = ( x 1 + x 2 + x 3 ) ( x
1 + x 2 + x 3 ) ( x 1 + x 2 + x 3 ) (c) ( x 1 + x 3 ) ( x 1 + x 2 + x 3 ) ( x 1 + x 2 ) = ( x 1 + x 2 ) ( x
2 + x 3 ) ( x 1 + x 3 ) 2) [10%] Use algebraic manipulation to find the minimum sum-of-
products expression for the function f = x 1 x 3 + x 1 x 2 + x 1 x 2 x 3 + x 1 x 2 x 3 3) [10%]
Draw the waveform of the function f given the waveforms of the inputs. f = x 1 x 3 + x 1 x 2 + x
2 x 3 + x 1 x 2 x 3 4) [10%] Use algebraic manipulation to find the minimum product-of-sums
expression for the function f = ( x 1 + x 2 + x 3 ) ( x 1 + x 2 + x 3 ) ( x 1 + x 2 + x 3 ) ( x 1 + x 2
+ x 3 )