Why do flip-flops require set-up times? What happens when the set-up time is not met?

Why do flip-flops require set-up times? What happens when the set-up time is not met?

why do

multiplexers come in sizes where the inputs are a power of 2 (e.g., 2-to-1, 4-to-1, 8-to-1, etc.)?

explain why the least-significant stage in a 4-bit adder-subtractor must be a full-adder and not a half-adder.

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explain how to design a circuit using a truth table to define the required outputs given all input conditions.

Using a 4-bit adder/subtractor circuit, carry out the binary operation (-7) + (-3). What can you conclude about the answer?

Why do computers use binary numbers?

Briefly explain why the carry-in bit (CIN) on the 4-bit binary adder discussed in the lecture is connected to ground.

How do you wire the D input of a D-type flip-flop so that the output toggles?

How many select lines are required for a 16-to-1 multiplexer? Explain how you determined your answer

Develop the Boolean equation for the output of a 2-to-1 multiplexer with select line S, inputs I0 and I1, and output Y. Use an apostrophe to indicate negation (e.g., use A’ for )

A 2-bit parallel adder has inputs of A1 = 1, A2 = 0, B1 = 1, B2 = 0, Cin . What are the values for S1, S2, C1, and Cout? Demonstrate how you derived your answer.

Using signed 8-bit representation, determine the result of 112 + 53. Show how you got your answer using binary arithmetic and the 2’s complement system.

What is the binary signed value for -67 using 8-bit, 2’s complement format? Show how you got your answer.