ECE251 hw6 - sol

# ECE251 hw6 - sol - NEW JERSEY INSTITUTE OF TECHNOLOGY DEPT...

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NEW JERSEY INSTITUTE OF TECHNOLOGY ACADEMIC YEAR 2008-2009 SEMESTER ` ECE251 DIGITAL DESIGN S OLUTION HW6 1. Truth table: ABC D WXY Z 0000 1001 0001 1000 0010 0111 0011 0110 0100 0101 0101 0100 0110 0011 0111 0010 1000 0001 1001 0000 1010 φφφ φ 1011 φφφ φ 1100 φφφ φ 1101 φφφ φ 1110 φφφ φ 1111 φφφ φ Outputs description in canonical forms: ) 15 , 14 , 13 , 12 , 11 , 10 ( ) 1 , 0 ( + = φ W ) 15 , 14 , 13 , 12 , 11 , 10 ( ) 5 , 4 , 3 , 2 ( + = X ) 15 , 14 , 13 , 12 , 11 , 10 ( ) 7 , 6 , 3 , 2 ( + = Y ) 15 , 14 , 13 , 12 , 11 , 10 ( ) 8 , 6 , 4 , 2 , 0 ( + = Z K-maps: 1

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01 11 00 01 10 10 11 AB CD 00 01 11 00 01 10 10 11 AB CD φ 1 1 1 1 1 1 C B A W = C B C B C B X = + = 00 01 11 00 01 10 10 11 AB CD 00 01 11 00 01 10 10 11 AB CD 1 1 1 1 1 C Y = D Z = Fig. 1 K-maps of the output functions A B C D W X Y Z Fig. 2. Circuit implementation 2. The design using a decoder does not make use of the don’t care conditions. 2
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ECE251 hw6 - sol - NEW JERSEY INSTITUTE OF TECHNOLOGY DEPT...

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