hw6_solns

hw6_solns - carry in(in the first 2-bit adder And/Or Set...

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University of Pittsburgh Department of Electrical and Computer Engineering Homework Assignment #6 Solutions 1) a) f(x1,x2,x3,x4) = 4 3 1 4 3 2 4 3 1 4 3 2 x x x x x x x x x x x x + + + AND3 inst AND3 inst1 AND3 inst2 AND3 inst3 OR4 inst4 NOT inst5 NOT inst6 VCC x2 INPUT VCC x1 INPUT VCC x3 INPUT VCC x4 INPUT f 1 OUTPUT f(x1,x2,x3,x4) = ) 4 3 )( 4 3 )( 2 1 ( x x x x x x + + + AND3 inst VCC x2 INPUT VCC x1 INPUT VCC x3 INPUT VCC x4 INPUT OR2 inst1 OR2 inst2 OR2 inst3 f 2 OUTPUT NOT inst4 NOT inst5

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f(x1,x2,x3,x4) = ) 4 3 4 3 )( 2 1 ( x x x x x x + + VCC x2 INPUT VCC x1 INPUT VCC x3 INPUT VCC x4 INPUT OR2 inst1 OR2 inst2 NOT inst5 AND2 inst AND2 inst3 NOT inst4 AND2 inst6 f 3 OUTPUT f(x1,x2,x3,x4) = ) 4 3 )( 2 1 ( x x x x + VCC x2 INPUT VCC x1 INPUT VCC x3 INPUT VCC x4 INPUT OR2 inst1 AND2 inst NOT inst4 f 4 OUTPUT XOR inst2 b) Waveform should look like this for all functions. 2) (5.10) Verify k k k k s y x c = Since sk = xk yk ck , it follows that xk yk sk = ( xk yk ) ( xk yk ck ) = ( xk yk ) ( xk yk ) ck = 0 ck = ck
3.) (5.23) x1 x2 s s0 s1 c c c c c s1 s0 c in c in y1 y2 y1 y2 x1 x2 Result is composed of s0 from first 2-bit adder and carry out, sum1, and sum0 from the second 2-bit adder. Alternatives: Use s from FA(z0,z1,z2) as y0, and s from HA(z7,z6) as

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Unformatted text preview: carry in (in the first 2-bit adder). And/Or: Set the carry in on the second 2-bit adder to the carry out from HA, and set x0 input to 0. 4. (6.3) 5. The problem asks for three solutions (using any type of logic gates). (6.5) Book solution: Other solutions: ) 3 ( 2 1 ) ( 2 1 ) 1 ( 2 1 ) 3 ( 2 1 w w w w w w w w w w f + + + = f 00 01 10 11 s1 s0 W1 W2 1 W3 ) ( 3 1 ) 2 ( 3 1 ) 2 ( 3 1 ) 1 ( 3 1 w w w w w w w w w w f + + + = (min cost) f 00 01 10 11 s1 s0 W1 W3 1 w2 w2 6) (6.10) )) ,..., 2 , 1 ( 1 ))( ,..., 2 , ( 1 ( ) 3 ,..., 2 , 1 ( wn w f w wn w f w w w w f + + = 7) xyz w 000 001 010 011 100 101 110 111 1 1 1 1 1 1 1 1 1 1 f 1 2 3 s1 s0 y z 1 1 s2 x 4 5 6 7 w 1 w’ w...
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hw6_solns - carry in(in the first 2-bit adder And/Or Set...

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