Question 1. Design a 4-bit combinational circuit for a 2’s complementer. The circuit generates at the output the 2’s complement of the input binary numbers.a) Complete the following truth table. A, B, C, D indicate the input binary number to be complement- ed using 2’s complement and W, X, Y, Z represent the output 2’s complement of the input binary number. The variable D is the least significant bit and A is the most significant bit of the binary number.b) Simplify the Boolean function W in its Sum-of-Products (SOP) form using a K-Map (you do not have to show the circuit) and provide its simplified Boolean expression.c) Show that the Boolean function W can be realized using exclusive-OR (XOR) gates and OR gates draw its corresponding logic circuit.d) Simplify the Boolean function Z in its Product-of-Sums (POS) form using a K-Map, provide its simplified Boolean expression and draw its corresponding logic circuit.
Question 1. Design a 4-bit combinational circuit for a 2’s complementer. The circuit generates at the output the 2’s complement of the input binary numbers.
a) Complete the following truth table. A, B, C, D indicate the input binary number to be complement- ed using 2’s complement and W, X, Y, Z represent the output 2’s complement of the input binary number. The variable D is the least significant bit and A is the most significant bit of the binary number.
b) Simplify the Boolean function W in its Sum-of-Products (SOP) form using a K-Map (you do not have to show the circuit) and provide its simplified Boolean expression.
c) Show that the Boolean function W can be realized using exclusive-OR (XOR) gates and OR gates draw its corresponding logic circuit.
d) Simplify the Boolean function Z in its Product-of-Sums (POS) form using a K-Map, provide its simplified Boolean expression and draw its corresponding logic circuit.
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