Question

3. Show the proof of Em(1,2,3,4,5,6,7)=x, +x2+x3 using boolean algebra

Answer 1

Given min term is m(1,2,3,4,5,6,7). From this min-term expression we will find out the Boolean expression by using a 3 variable K-map as follows. + X1 0001 11 10 11 1 1 1 1 1 1 1 1 1 1 1 X1 From the above K-Map we can easily derive the expression as X1 + X2 + X3 So Zm(1,2,3,4,5,6,7) = X1 + X2 + X3

Another method: The given expression is Em(1, 2, 3, 4, 5, 6, 7) (Let this is y If We will write ist in the oforms of pos terms then tay - X, X₂ X3 + X, X₂ X3 + X1 X₂ X3 + X, X2 X₃ +X17 X tx, x273 +x, x27, Applying AND Distributive laws = X, X 2 X ₂ + X1 X2 (73 443) + x, 72 (73 473) + X1 X2 (83 783) Applying inverse Law & = X1 X2 X3 + X1 X2 + X1 X2 +X1X2 - X, (7243 +42) + X 2 X 2 X2) = 7, 42+72) (X2+X3 ) + x1 =X, (x2 +X3 ) + XI = (x1+x, ) (x1+x2+7) = X1 + X2 TX₂ So I m (1, 2, 3, 4, 5, 6, 7) = x + x2 +43]

AND Distributive Law & TA+ BC = (A+B) (A + c)] INVERSE LAW TATÃ = 1