This question is concerned with the optimization of logic functions using combinational circuit components. Use the cost definition of logic circuits presented in the course. Suppose that the input variables are not available in their complemented form. Derive a minimum-cost realization of the four-variable function that is equal to 1 if any three or all four of its variables are equal to 1 (called the majority function). Use Karnaugh maps to minimize the function and implement the circuit using NAND gates only, with a maximum fan-in of 4. Provide the final cost of the circuit.

Simplify the following Boolean function using four variable K-map. F(A, B, C, D) = Σ (0, 1, 2, 5, 8, 9, 10) (b) Draw the logic diagram with AND-OR-NOT gates. (c) Draw the logic diagram with NAND gates. (d) Draw the logic diagram with NOR gates using Digital Logic in computer architecture.

Consider the circuit B 1. Derive the Boolean equations representing the outputs D = B = 2. Complete a truth table for the circuit Are both outputs minimized to the fewest number of literals/gates? Use the next page as workspace if needed. 3.

CREATING A CIRCUIT DIAGRAM Questions 4 and 5 refer to the function defined by the following truth table: w result 00001 00010 00110 00101 01101 01111 01010 0100 0 1 1000 1 1 0 1 0 1 111 0 11101 1 010 1 0 1 1 0 1 - 1 0010 1 000 1 Question 4 Fill in the values and draw the groupings of the Karnaugh Map. ५३ Wx 00 01. 11 10 00 01 11 10