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Hw2-sol - EE 3320 DIGITAL CIRCUITS HOMEWORK 2 SOLUTIONS...

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EE 3320 DIGITAL CIRCUITS HOMEWORK # 2 SOLUTIONS
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Solution 1 Simplify the following Boolean function using K-maps to get the smallest implementation: ( ) ( ) ( ) ̅ ̅ ( )( ̅ ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ̅ ̅ ( )( ̅ ) ̅ ̅ ̅ ( ) ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ 00 01 11 10 ̅ ̅ 00 1 ̅ 01 1 1 1 1 11 1 1 1 1 ̅ 10 1 1 1 1 ̅ ( ) ̅
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( ) ( ) ( ) ( ) ̅ ̅ ̅ ̅ 00 01 11 10 00 X 0 0 ̅ 01 X ̅ ̅ 11 0 0 0 ̅ 10 0 X ( ̅ )( ̅ ̅ ̅ )( ̅ ) ( ) ( ̅ )( ̅ ̅ ̅)( ̅)
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Solution 2 Use multiple output minimization technique to find a minimum two-level AND-OR circuit for the functions given below. Determine the number of gates and gate inputs for each circuit. You may assume that dual rail inputs are available . ( ) ( ) ( ) ( ) ( ) ( ) Considering the minterms: ( ) 00 01 11 10 00 1 x 0 x 01 0 1 1 1 11 x 0 x 0 10 1 0 x 0 ( ) 00 01 11 10 00 x 0 x 0 01 0 1 1 0 11 x x x 1 10 0 0 1 1 ( ) ̅ ̅ ̅ ̅ ̅ ( ) ̅ Total of 6 Gates with 16 Gate Inputs
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Considering the maxterms: ( ) 00 01 11 10 00 1 x 0 x 01 0 1 1 1 11 x 0 x 0 10 1 0 x 0 ( ) 00 01 11 10 00 x 0 x 0 01 0 1 1 0 11 x x x 1 10 0 0 1 1 ( ) ( ̅ )( ̅ )( ̅ ̅ )( ̅ ̅) ( ) ( ̅ )( ̅ )( ̅ )( ̅ )
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