You can express any logic function f as f(x,y,z,...)=x f(x=1, y, z, ...) + x' f(x=0,...

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You can express any logic function f as f(x,y,z,...)=x f(x=1, y, z, ...) + x' f(x=0, y, z, ...). This is called Shannon's Expansion. = For example, f(w1, W2, W3, W₁) = W₁ ƒ (W₁) + W₁f (w₁), where ƒ (w₁ ) = f(w₁ 0, W2, W3, W4) and f(w₁) = f(w₁ = 1, W2, W3, W4), as illustrated in the figure below W1 W2 W3 f(w₁) W4 0 f f(w₁) (a) In case the decomposition yields f(w₁) = 1, then you can replace the multiplexer in the figure by a single logic gate. Show this circuit. (b) Repeat (a) for the case where f (w₁) = 0. Activate W You can express any logic function f as f(x,y,z,...)=x f(x=1, y, z, ...) + x' f(x=0, y, z, ...). This is called Shannon's Expansion. = For example, f(w1, W2, W3, W₁) = W₁ ƒ (W₁) + W₁f (w₁), where ƒ (w₁ ) = f(w₁ 0, W2, W3, W4) and f(w₁) = f(w₁ = 1, W2, W3, W4), as illustrated in the figure below W1 W2 W3 f(w₁) W4 0 f f(w₁) (a) In case the decomposition yields f(w₁) = 1, then you can replace the multiplexer in the figure by a single logic gate. Show this circuit. (b) Repeat (a) for the case where f (w₁) = 0. Activate W

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a If fw 1 then the multiplexer can be replaced by a si... View the full answer