Q1 Design a circuit that counts the number of 0's present in 3 inputs A, B and C. Its output is a two-bit number which are X1 and Xo, representing that count in binary. (a) (i) Construct the truth table for this circuit. Find the minimize logic equations for output X1 and Xo. Use the Karnaugh map and Boolean algebra to simplify the expressions. (b) Given the Boolean expression, m = (x + y)(y + z)(x + y)(9 + 2) (i) Construct a truth table for the output, m. (ii) Derive the minimal sum of product (MSOP) for the output, m. (iii) Draw the related logical circuit for output, m.

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