For the logic circuit given below, for
a) input $A = 0$ and input $B = 1$ , and
b) input $A = 1$ and input $B = 1$ , the output $E$ is respectively

Question

For the logic circuit given below, for a) input A = 0 and input B = 1 , and b) input A = 1 and input B = 1 , the output E is respectively

TestHub · Accepted Answer

From the given logic circuit diagram, we can determine the Boolean expressions for the intermediate outputs $C$ and $D$ , and the final output $E$ .

The top AND gate receives inputs $A$ and $B$ . Therefore, its output is:
$C = A \cdot B$

The bottom AND gate receives input $B$ and the inverted input of $A$ (which is $\overset{ˉ}{A}$ ). Therefore, its output is:
$D = \overset{ˉ}{A} \cdot B$

The OR gate receives inputs $C$ and $D$ . The final output $E$ is:
$E = C + D$
$E = A \cdot B + \overset{ˉ}{A} \cdot B$

Simplifying the Boolean expression for $E$ :
$E = B \cdot (A + \overset{ˉ}{A})$
Since $A + \overset{ˉ}{A} = 1$ , we get:
$E = B \cdot 1 = B$

Now, evaluating the given conditions:
a) For input $A = 0$ and $B = 1$ :
$E = B = 1$

b) For input $A = 1$ and $B = 1$ :
$E = B = 1$

Thus, the output $E$ is one and one respectively.

Answer: one and one.

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