Question

2. [20 points] A circuit with 4 inputs has to realize the following 3 functions z, w)-n (0, 1,3,4,9, 11) g (x, y,z, w)-2 (5, 8,9, 10, 11, 12, 13, 14, 15) In what follows the cost a circuit is defined as: Number of gates used + mumber of inputs to these es but not counting NOTs. So, assume that input variables are available in both complemented and un-complemented forms. (a) [10 points] Find simple SOP expressions using K-maps for each of the functions f, g and h, (b) [10 points] Design the minimum cost circuit combining terms from the three functions and separately, Draw the circuits for each of f.g and h. What are their costs? compare its total cost with the sum of the costs of the circuits you found in (a). Draw the combined circuit.

Answer 1

K - maps F(x, y, z, w) = (0, 1, 3, 4, 9, 11) max terms given implies for boP expression, we need minterms so, minterms are the rest sigma (2, 5, 6, 7, 8, 10, 12, 13, 14, 15) \r\n F = xw + yw + zw \r\n cost = 4gates + 9 inputs = 13 implies g(x, y, z, w) = sigma (5, 8, 9, 10, 11, 12, 13, 14, 15) \r\n g = x + yzw \r\n cost = 2gates + 5inputs = 7 implies h(x, y, z, w) = xw + yzw + x�yz + x�zw� \r\n h = xw + xyz + xzw \r\n cost = 4gates + 11inputs = 15 F = xw + yw + zw g = x + yzw h = xw + xyz + xzw Minimized circuit Total cost of circuit in part(a) 13 + 7 + 15 = 35 Toatl cost for this circuit is 10gates + 23 = 33

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