Assignment
1. For the following circuits, put them into Product of Maxterms and Sum of Minterms forms. I do not care which of the two ways I mentioned you use to do it (make a truth table, or manipulate into product of sums/sum of products form). Remember that for complex equations, you may want to evaluate subfunctions first.
a. G = A‾*B*C‾*D+D*C‾(A‾+B‾)+A‾*C(B‾+D‾)+A*B‾*C‾*D
b. F = [{(A⊕D)*C}‾+B)*{A‾*B+(C*D)‾}]‾ note: there is no XNOR here, but there are 3 NANDs.
c. H = B‾*C(A⊕D)‾+A*B‾*C‾*D+[A‾*C‾*D+D*B‾(A‾+C‾)]‾
2. We wish to implement the following circuit:
A jet has 4 engines, A and B on the left wing, C and D on the right wing. Each engine gives a FAIL signal which is TRUE if the engine is broken, and is FALSE if the engine is working fine. The plane can fly as long as at most 1 engine on each wing is broken. We want a signal EMERGENCY, which is true if the plane can no longer fly.
a. Would the Sum of Minterms or Product of Maxterms be smaller for this circuit?
b. Write the Boolean equation for EMERGENCY. It should be in the format identified in 2a above (Sum of Mintenns or Product of Maxterms, whichever is smaller)
c. Draw a schematic for your equation using only NAND or only NOR gates, whichever results in less logic.
3. For the circuit given below, show the output ("F") waveform for the transition (A=0,B=1,C=0) to (A=1,B=1,C=0). Assume all gates (inverters, ANDs, ORs, XORs) have a delay of 5ns. Reminder: You cannot calculate F directly. You must figure out the internal signals first.
4. For the following truth tables, provide the corresponding Boolean equation. Do not simplify the equations.
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A
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B
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C
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Output 1
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0
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0
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0
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0
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0
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0
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1
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1
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0
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1
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0
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0
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0
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1
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1
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0
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1
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0
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0
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1
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1
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0
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1
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0
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1
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1
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0
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1
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1
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1
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1
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0
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A
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B
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C
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Output 1
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0
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0
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0
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0
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0
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0
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1
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1
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0
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1
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0
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0
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0
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1
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1
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0
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1
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0
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0
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1
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1
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0
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1
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0
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1
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1
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0
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1
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1
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1
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1
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0
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A
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B
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Output 3
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0
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0
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1
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0
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1
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1
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1
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0
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0
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1
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1
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I
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