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# Hw1-sol - EE 3320 DIGITAL CIRCUITS HOMEWORK 1 SOLUTIONS...

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EE 3320 DIGITAL CIRCUITS HOMEWORK # 1 SOLUTIONS

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Solution 1 Reduce the following function to the SOP form: ( ) ∑( ) ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ( ̅ ) ̅( ̅ ) ̅ ̅ ̅ ̅ ̅ ̅ ̅ ( ̅ ̅) ̅ ̅ ( ̅ )( ̅ ̅) ̅ ̅ ( ̅ ̅) ̅ ̅ ̅ ̅ Solution 2 Simplify the following function to POS from: ( ) ∏( ) ( ̅ )( ̅ )( ̅ ̅)( ̅ ̅ ̅) ( ̅ )( ̅ )(( ̅ ̅) ̅) ( ̅ )( ̅ )( ̅ ̅) ( ̅ )( ̅ ( )( ̅)) ( ̅ )( ̅ ̅ ̅) ( ̅ )( ̅ ̅) ( ̅ )( ̅ )( ̅ )
Solution 3 Determine the minimum number of inverters, 2-input ANDs and ORs needed to implement the Boolean function given below: ( ) ∑( ) The reduced SOP form is as follows: ̅ ̅ ̅ ̅ The reduced POS form is as follows: ( )( ̅ ̅)( ̅) 2 input AND Gates 2 input OR Gates Inverters SOP 4 2 3 POS 2 3 3

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Solution 4 Convert the following expression to Canonical SOP and Canonical POS forms. Show all steps. ( ) ( ̅ ) ̅̅̅̅̅̅̅̅̅̅̅̅ ̅ ̅ ̅ ̅ ( ̅ ) ̅̅̅̅̅̅̅̅̅̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ Method 1: Express ( ̅ ̅ ̅ ̅) in the k-map ̅ ̅ ̅ ̅ 00 01 11 10 ̅ ̅ 00 1 1 1 1 ̅ 01 1 11 1 1 ̅ 10 1 1 1 1 For Canonical SOP: ∑( ) ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ For Canonical POS: ( ) ( ̅ ̅)( ̅ ̅ )( ̅ ̅ ̅)(
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Hw1-sol - EE 3320 DIGITAL CIRCUITS HOMEWORK 1 SOLUTIONS...

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