Circuit design example

What will a combinational logic circuit look like using any basic gates having the output=1 when the input=110 and 101?

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• Hint: $x \wedge (y \oplus z)$ – Dilip Sarwate May 23 '13 at 12:07
• As for all questions that smell of homework: what have you done or found out so far, at what point are you stuck? – Wouter van Ooijen May 23 '13 at 12:42
• Hint: You can use a Karnaugh map to easily figure this out. Not sure if they still teach that or not. – Jason R May 23 '13 at 13:52

• A Karnaugh map is only necessary for deriving the function from raw inputs and outputs, or as an optimization tool for finding a minimal function. Here, the function is already given as a sum of products: the output is to be 1 if the inputs are 101 or 110 (and presumably 0 if the inputs are otherwise). From this you can go straight to gates (perhaps after some algebra). xy'z + xy'z -> x(y'z + yz'), and perhaps -> x(y xor z). – Kaz May 23 '13 at 19:12