Question

1. determine the output, x, for a 2 - input and gate with the input waveforms shown in figure 3 - 78. show the proper relationship of output to inputs with a timing diagram.

Explanation:

Step1: Recall AND gate logic

The output of an AND gate is defined as \(X = A \cdot B\) (or \(X = A \land B\)), where \(X=1\) only if both \(A=1\) and \(B=1\); else \(X=0\).

Step2: Compare input waveforms

Align the two input waveforms by time intervals. For each interval, check if both \(A\) and \(B\) are high.

Step3: Generate output waveform

For each time interval:

• If \(A=1\) and \(B=1\), set \(X=1\)
• If either \(A=0\) or \(B=0\), set \(X=0\)

Step4: Plot timing diagram

Align the output waveform \(X\) vertically with the input waveforms, matching the time intervals from Step 2.

Answer:

The output waveform \(X\) is high (1) only during the time intervals where both input waveforms \(A\) and \(B\) are high (1), and low (0) at all other times. The timing diagram below illustrates this:

Time Interval	Input \(A\)	Input \(B\)	Output \(X = A \cdot B\)
2	1	1	1
3	0	1	0
4	0	0	0
5	1	0	0
6	1	1	1
7	0	1	0
8	0	0	0

Visual timing diagram alignment:

• \(A\): High → High → Low → Low → High → High → Low → Low
• \(B\): Low → High → High → Low → Low → High → High → Low
• \(X\): Low → High → Low → Low → Low → High → Low → Low