Answer on Question #43450, Math, Discrete Mathematics
write the following boolean expressions in an equivalent sum of product canonical form in three variables x1, x2, and x3:
1. x1*x2 ?
2. x1 ⊕ x2 ?
3. (x1 ⊗ X2) * X3
Solution.
We will express each function as sum of minterms.
1. f(x1,x2,x3)=x1x2=x1x2(x3+x3′)=x1x2x3+x1x2x3.
2. f(x1,x2,x3)=x1⊕x2=x1′x2+x1′x2=x1′x2(x3+x3′)+x1′x2(x3+x3′)=x1′x2x3+x1′x2x3′+x1′x2x3′.
3. f(x1,x2,x3)=(x1⊕x2)′x3=(x1′x2+x1′x2)′x3=(x1+x2′)(x1′+x2)x3=x1x1′x3+x1x2x3+x1′x2′x3+x2x2′x3=x1x2x3+x1′x2′x3.
Answer:
1. f(x1,x2,x3)=x1x2x3+x1x2x3.
2. f(x1,x2,x3)=x1′x2x3+x1′x2x3′+x1′x2x3+x1′x2x3′.
3. f(x1,x2,x3)=x1x2x3+x1′x2′x3.
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