Given the following function in product of sums form, not minimized. F(W, X, Y,

Question

Given the following function in product of sums form, not minimized.

F(W, X, Y, Z) = (W + !X + !Y) (!W + !Z) (W + Y)

a) Express the function in the canonical sum-of-products form. Use "little m" notation.

b) Re-express the function in minimized sum-of-products form.

c) Express !F in minimized sum-of-products form.

d) Re-express !F in minimized product-of-sums form.

Explanation / Answer

F'=(W'+X'+Y'+Z)(W'+X'+Y+Z)(W'+X+Y'+Z)(W'+X+Y+Z)(W+X+Y'+Z')(W+X+Y'+Z) (USE DEMORGAN'S THEOREM) (F')'=F=WXYZ' + WXY'Z' + WX'YZ' + WX'Y'Z' + W'X'YZ + W'X'YZ' ----(*) ==>F=m14+m12+m10+m8+m3+m2 ----a W X Y Z FROM(*), 0 0 0 0 0 F=WXZ'(Y+Y) + WX'Z' +W'X'Y 1 0 0 0 1 =(WXZ' +WX'Z') + W'X'Y =WZ' + W'X'Y ----b 2 0 0 1 0 3 0 0 1 1 FROM ?D

Related Questions

Navigate

• Browse (All)
• Browse G
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.