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ECE251 hw6

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

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NEW JERSEY INSTITUTE OF TECHNOLOGY DEPT. OF ELECTRICAL & COMPUTER ENGINEERING ACADEMIC YEAR 2010-2011 SEMESTER 1 ECE251 DIGITAL DESIGN HW 7 1. Design a combinational circuit with five inputs and two outputs. The inputs are D 2 , D 1 , D 0 , and C 1 and C 0 . The circuit calculates the remainder R 1 and R 0 of the division of the binary number D 2 D 1 D 0 (called the dividend) by the divisor C 1 C 0 . For example, if D 2 D 1 D 0 =111 and C 1 C 0 =10, then R 1 R 0 =01 (that is, the remainder of 7 divided by 2 is 1). Note that division by zero will never be requested. 2. Compute a hazard-free minimal Boolean function for the following canonical forms: (a) = ) 14 , 13 , 11 , 9 , 7 , 6 , 5 , 4 , 0 ( ) , , , ( D C B A F (b) = ) 15 , 13 , 9 , 8 , 7 , 5 , 3 , 1 , 0 ( ) , , , ( D C B A F 3. List all the static hazards in the SOP implementation of D A C A B A F + + = . Compute a minimal hazard-free function that will eliminate all these hazards. 4. List all the static hazards in the POS implementation of ) )( )( )( ( D C B D B A D C B D C A F + + + + + + + + = . Compute a minimal hazard-free function that will eliminate all these hazards.

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