a) Table Q.2(a) shows the truth table for an output function Y (A, B, C, D) 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 B 0 0 0 0 1
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DIGITAL ELECTRONICS
a) Table Q.2(a) shows the truth table for an output function Y (A, B, C, D) 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 B 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 Table Q.2(a) Inputs с 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 D 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 Output Y 0 0 1 1 0 0 0 0 1 1 1 1 1 0 0 1 (i) Write the standard SOP expression for Y. (2 marks) (ii) Determine the minimized SOP expression for Y by using K-map. (4 marks) (iii) Implement the circuit for Y by using MUX 4:1 and NAND gates only. (4 marks)
(b) A ROM chip is used to implement the Boolean functions listed below. W(A, B, C) = m(0,2,4,6) X(A, B, C) = IIM (1,3,5,7) Y(A, B, C) = ABC + ABC + ABC + ABC Z(A,B,C) = (A + B)(A+B+C) (i) What is the ROM size required? (2 marks) (ii) Write down the truth table for the ROM address and data lines. (4 marks) (iii) Implement the ROM circuit using a 3-to-8 active high decoder. Draw and label the connections clearly. (4 marks)