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A Boolean function F defined on three input variables X, Y and Z is 1 if and only if number of 1(one) inputs is odd (e.g., F is 1 if x = 1, Y = 0, Z = 0). Draw the truth table for the above functions and express it in canonical sum-of- products form

1 Answer

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Best answer

The output is 1, only if one of the inputs is odd. All the possible combinations when one of inputs is odd are X = 1, Y = 0, Z = 0 X = 0, Y = 1, Z = 0

X = 0, Y = 0, Z = 1

For these combination output is 1, otherwise output is 0. Preparing the truth table for it, we get

Adding all the minterms for which output is 1, we get 

X’Y’Z + X’YZ’ + XY’Z’= F 

This is desired Canonical Sum-of-Products form.

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