Question

Consider the digital circuit shown below, a number (B) is converted into its 4-bit binary equivalent $\left(B_3{B}_2{B}_1{B}_0\right)$ and then applied to the addend bits of the adder as shown below.



Which of these given statement(s) is/are correct?

• A. If number B is 15, then the output $S_3{S}_2{S}_1{S}_0$ is 1001
• B. If number B is 13, then the output $S_3{S}_2{S}_1{S}_0$ is 1011
• C. If number B is 7, then the output $S_3{S}_2{S}_1{S}_0$ is 1000
• D. The bit $C_4$ will be reset in all above case

Answer 1

Answer: (A), (B)

If number B is 13, then the output $S_3{S}_2{S}_1{S}_0$ is 1011

For (a)
$B=15$
$B_3{B}_2{B}_1{B}_0=1111$

$1⨁B_3=1⨁B_2=1⨁B_1=1⨁B_0=0$

Diagram

$\Rightarrow$ $S_3{S}_2{S}_1{S}_0=1001$

For (b)
$B=15$
$B_3{B}_2{B}_1{B}_0=1101$

$1⨁B_3=1⨁B_2=1⨁B_0=0,1⨁B_1=1$

Diagram

$\Rightarrow$ $S_3{S}_2{S}_1{S}_0=1011$

For (b)
$B=7$
$B_3{B}_2{B}_1{B}_0=0111$

$1⨁B_2=1⨁B_1=1⨁B_0=0,1⨁B_3=1$

Diagram

$\therefore$ $S_3{S}_2{S}_1{S}_0=0001$