HW4_soln

HW4_soln - ECE 15A Homework 4 Solutions 3(a f(A,B,C = AB'C BC A'C We know that(AND OR NOT gates are functionally complete and so if our function

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Unformatted text preview: ECE 15A Homework 4 Solutions 3.(a) f(A,B,C) = AB'C+BC'+A'C' We know that (AND, OR, NOT) gates are functionally complete and so if our function can be used to make all these 3 gates, then the function f is also functionally complete. Let our inputs be X and Y. NOT Gate We need to make output = X'. Put A=0, B=1 and C = X Then f = 0.0.X + 1.X' + 1.X' = X' +X' = X' So f-gate becomes a NOT gate! AND gate We need to make output = XY Put A=Y, B=X and C = Y' 1 Then f = YX'Y' + XY + Y'Y = YY'X' + XY + 0 = 0.X' + XY = XY So, f-gate becomes an AND gate! OR gate We need to make output = X+Y Put A = X, B= Y and C = Y' Then f = XY'Y' + YY + X'Y = XY' + Y + X'Y = XY' + Y ( 1+ X') = XY' + Y.1 = XY' + Y.(1+X) ( because 1+X =1) = XY' + YX + Y = X( Y' +Y) + Y (Using commutative and distributive properties) =X+Y So, we can also make an OR gate! So, f-gate is a universal gate. (b) Done above. 2 3 6. f(a,b,c,d)=a'b'c'd+a'b'cd'+a'bc'd+a'bcd+a'b'c'd+ab'cd+abcd' a) show kmap ab cd 00 01 00 1 1 01 0 1 11 0 0 10 0 1 11 0 1 0 1 10 1 0 1 0 b) list all prime implicants a'b'd', a'b'c', a'bd, a'c'd, ab'd, abcd', b'c'd c) list all essential prime implicants a'b'd', a'bd, abcd', ab'd' 4 5 6 7 8 9 10 11 ...
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This note was uploaded on 01/20/2011 for the course ECE 15A taught by Professor M during the Winter '08 term at UCSB.

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HW4_soln - ECE 15A Homework 4 Solutions 3(a f(A,B,C = AB'C BC A'C We know that(AND OR NOT gates are functionally complete and so if our function

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