HW6_Solutions - ECE 2030 E,F Homework #6 - Solutions (1)...

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Unformatted text preview: ECE 2030 E,F Homework #6 - Solutions (1) Textbook #4-1 Design a 2-level (SOP), 2-digit binary adder with carry-in and carry-out, according to the following formulas. Si = AiBiCi + AiBiCi + AiBiCi + AiBiCi C(i+1) = AiBi + AiCi + BiCi Solution: First notice that the inputs to the circuit are A0, B0, A1, B1, C0 and the outputs are S0, S1, C2. So, we must find S0, S1, and C2 as SOP functions of the input variables. S0 = A0B0C0 + A0B0C0 + A0B0C0 + A0B0C0 (a) S1 = A1B1C1 + A1B1C1 + A1B1C1 + A1B1C1 (b) C1 = A0B0 + A0C0 + B0C0 (c) C1 = (A0B0 + A0C0 + B0C0) = (A0+B0)(A0+C0) (B0+C0) = A0B0 + B0C0 + A0C0 (d) Substitute (c) and (d) into (b) to get: S1 = A1B1 (A0B0 + A0C0 + B0C0) + A1B1 (A0B0 + B0C0 + A0C0) + A1B1 (A0B0 + B0C0 + A0C0) + A1B1 (A0B0 + A0C0 + B0C0) (e) = A0 B0A1B1 + C0A0A1B1 + C0B0A1B1 + A0 B0A1B1 + C0B0A1B1 + C0A0A1B1 + A0B0 A1B1 + C0B0A1B1 + C0A0A1B1 + A0B0A1B1 + C0A0A1B1 + C0B0A1B1 (f) C2 = A1B1 + A1C1 + B1C1 (g) Substitute (c) into (g) to get: C2 = A1B1 + A1(A0B0 + A0C0 + B0C0) + B1(A0B0 + A0C0 + B0C0)...
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This note was uploaded on 01/16/2012 for the course ECE 2030 taught by Professor Wolf during the Fall '07 term at Georgia Institute of Technology.

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HW6_Solutions - ECE 2030 E,F Homework #6 - Solutions (1)...

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