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Logic Gates

Let X = ABC +...

Question

Let $X = ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ A B C + ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ B C A + ¯ ¯¯¯¯¯¯¯¯¯¯¯¯ ¯ C A B .$ Evaluate X for

(a) $A = 1, B = 0, C = 1,$ (b) $A = B = C = 1,$ and (c) $A = B = C = 0.$

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Solution

Since $X = A B C + B C A + C A B$

(a) $A = 1, B = 0, C = 1$

$X = 1 (1.1) + 0 (1.1) + 1 (1.0)$

$= 1.0 + 0.0 + 1.1 = 0 + 1 = 1$

(b) $A = B = C = 1$

$X = 1 (1.1) + 1 (1.1) + 1 (1.1)$

$= 1.0 + 1.0 + 1.0 = 0 + 0 + 0 = 0$

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