ECE251 hw4 - sol

# ECE251 hw4 - sol - NEW JERSEY INSTITUTE OF TECHNOLOGY DEPT...

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NEW JERSEY INSTITUTE OF TECHNOLOGY ACADEMIC YEAR 2010-2011 SEMESTER 1 EE251 DIGITAL DESIGN S OLUTION HW4 1. The K-map: 00 01 11 10 0 1 1 1 1 1 1 AB C Figure 1: K-map for Pb. 1 The simplified function: B A C F + = 2. Map of the original function: 00 01 11 10 0 1 xy z 1 1 1 1 xy z y x z y x Figure 2: K-map of the given function K-Map of the simplified function: 00 01 11 10 0 1 xy z 1 1 xy z x 1 1 Figure 3: Minimal cover Therefore: z x xy F + = . 3. The K-map: 1

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00 01 11 00 01 10 10 11 1 1 1 1 1 1 1 * * * * = Distinguished cell D B D C A ABC AB CD Figure 4: Minimal cover for Pb. 3 Therefore, D C A ABC D B F + + = . 4. The K-map: 00 01 11 00 01 10 10 11 AB CD 0 0 0 0 0 0 0 0 0 0 D B A + + D B + D C + C A + Figure 5: One possible minimal cover for Pb. 4. Therefore: ) )( )( )( ( D B A D C C A D B F + + + + + = . 5. The function we need to implement is: ) 15 , 14 , 13 , 11 , 10 , 7 , 6 , 5 ( ) , , , ( = = F D C B A G The K-map: 2
00 01 11 00 01 10 10 11 AB CD 1 1 1 1 1 1 1

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ECE251 hw4 - sol - NEW JERSEY INSTITUTE OF TECHNOLOGY DEPT...

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