ECE251 hw7 - sol

# ECE251 hw7 - sol - NEW JERSEY INSTITUTE OF TECHNOLOGY DEPT...

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NEW JERSEY INSTITUTE OF TECHNOLOGY ACADEMIC YEAR 2008-2009 SEMESTER 1 ECE251 DIGITAL DESIGN S OLUTION HW7 1. The truth table ( φ denotes a don’t care) is shown on the next page. The canonical representation of the outputs is: ) 28 , 24 , 20 , 16 , 12 , 8 , 4 , 0 ( ) 31 , 30 , 22 , 19 , 14 , 7 , 6 ( ) 28 , 24 , 20 , 16 , 12 , 8 , 4 , 0 ( ) 23 , 11 ( 0 1 + = + = φ R R K-maps (5 variable): 00 01 11 00 01 10 10 11 00 01 11 00 01 10 10 11 0 1 D D 0 1 D D 0 1 C C 0 1 C C 0 2 = D 1 2 = D 00 01 11 00 01 10 10 11 00 01 11 00 01 10 10 11 0 1 D D 0 1 D D 0 1 C C 0 1 C C 0 2 = D 1 2 = D 1 1 1 ) ( 0 1 2 0 1 2 0 1 0 1 0 1 2 0 1 0 1 2 1 D D D D D D C C C C D D D C C D D D R + = + = 1 1 1 1 1 1 1 8 cell cube 0 1 0 1 2 1 2 1 2 1 0 0 0 1 0 1 2 1 0 1 2 1 0 1 2 0 0 0 )] ( [ C C D D D D D D D C C D C C D D D C D D D C D D D C D R + + + = + + + = Figure 1: K-maps of the two output functions 1

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The circuit: 2 n D 2 D 1 D 0 C 1 C 0 R 1 R 0 0 000 00 φφ 4 001 00 φφ 8 010 00 φφ 1 2 011 00 φφ 1 6 100 00 φφ 2 0 101 00 φφ 2 4 110 00 φφ 2 8 111
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ECE251 hw7 - sol - NEW JERSEY INSTITUTE OF TECHNOLOGY DEPT...

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