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ECE251 hw3

# ECE251 hw3 - (b wz xy z z y x to three literals(c CD A A B...

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NEW JERSEY INSTITUTE OF TECHNOLOGY DEPT. OF ELECTRICAL & COMPUTER ENGINEERING ACADEMIC YEAR 2010-2011 SEMESTER 1 ECE251 DIGITAL DESIGN HW 3 1. Simplify the following expressions using Boolean algebra: (a) ( 29 y x x w x w yz x z y x x z y x w f + + + + + = , , , (b) ( 29 ( 29 ( 29 ( 29 z x y x z x x z z z y z y x f + + + + = , , (c) ( 29 D B A CD D A A D C B A D AB D A AB D C B A f + + + + + + + = , , , (d) ( 29 ( 29 ( 29 ( 29 ( 29 C A B A C B A A AB BC AB A B C B A f + + + + + + + = , , 2. Find the complement of the following expressions: (a) y x y x + (b) E D C B A + + ) ( (c) ) )( )( ( y x z x z y x + + + + 3. Obtain the truth table of the following functions and express each function in sum of minterms and product of maxterms: (a) ) )( ( xz y z xy + + (b) ) )( ( C B B A + + (c) z x w z wx y wx z y + + + 4. Find the minimum equivalent circuit for the one shown in Figure 1. 1

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A B C F Figure 1: Circuit for Pb. 4 5. Convert the following expressions to the other canonical (standard) form: (a) = ) 7 , 3 , 1 ( ) , , ( z y x F (b) = ) 12 , 6 , 4 , 3 , 1 , 0 ( ) , , , ( D C B A F 6. Reduce the following Boolean expressions to the indicated number of literals: (a) C A ABC C A + + to three literals
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Unformatted text preview: (b) wz xy z z y x + + + + ) ( to three literals (c) ) ( ) ( CD A A B D C D B A + + + to one literal 7. Prove that: (a) y x y x ⊕ = ⊕ (b) x x = ⊕ 1 (c) = ⊕ x x (d) 1 = ⊕ x x 8. Given the following circuit: 2 A B C D F Figure 2: Circuit for Pb. 8 (a) Determine the raw (i.e. as is) Boolean function of the circuit. (b) Simplify the Boolean function and express it as sum of products. (c) Show the simplified circuit by implementing your solution from (b). 9. Prove that the circuit of Figure 3 implements a XOR function. x y F Figure 3: Circuit for Pb. 9 10. Simplify the following functions: (a) ) )( ( y x y x + + (b) xyz yz x z y + + (c) ) )( )( ( z y x z y x y x + + + + + 3...
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ECE251 hw3 - (b wz xy z z y x to three literals(c CD A A B...

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