ECE251 hw5 - sol

ECE251 hw5 - sol - A =1 B =1 Since F =1 under these...

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NEW JERSEY INSTITUTE OF TECHNOLOGY ACADEMIC YEAR 2008-2009 SEMESTER 1 ECE251 DIGITAL DESIGN S OLUTION HW5 1. [ ]( 29 D AC C B D A AC D D C B A F + + = + + + = ) ( ) ( . 2. The K-map: 00 01 11 00 01 10 10 11 AB CD 1 1 1 1 1 D C B A D C B ACD Fig. 1 Minimal SOP: ACD D C B D C B A F + + = 3. The K-map: 1

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00 01 11 00 01 10 10 11 AB CD 0 0 0 0 0 0 0 C B A + + D C A + + D B A + + D C B A + + + Fig. 2 Minimal POS: ) )( )( )( ( D C B A D B A D C A C B A F + + + + + + + + + = 4. Let: A =1 if it rains the next morning; A =0 otherwise. B =1 if Jean’s mother joins; B =0 otherwise. C =1 if Jean’s mother pays for the joint lunch; C =0 otherwise. The function displaying the necessary conditions for going to the park, using the above variables, is: C ABC B A F + + = . This can be simplified to: C AB B A AB C C C B A F + + = + + + = ) )( ( The actual conditions on the day of the trip were:

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Unformatted text preview: A =1 B =1 Since F =1 under these conditions, they will all go to the park. 5. Truth table: 2 AB C X Y 000 1 001 1 010 011 1 100 101 1 110 1 1 111 1 1 K-maps: 00 01 11 10 1 00 01 11 10 1 AB AB C C 1 1 1 1 1 1 1 1 AB AB AC BC B A BC AC AB X + + = B A AB Y + = Fig. 3 K-maps of X and Y The functions X and Y can be written in the following way: ) ( B A C AB X + + = B A AB Y + + = The implementation: 3 A B C X Y Fig. 4 Circuit implementation 4...
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ECE251 hw5 - sol - A =1 B =1 Since F =1 under these...

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