Question

A number in 4-bit two's complement representation is $X_3{X}_2{X}_1{X}_0$. This number when stored using 8-bits will be

• A. $0000X_3{X}_2{X}_1{X}_0$
  
• B. $1111X_3{X}_2{X}_1{X}_0$
• C. $X_3{X}_3{X}_3{X}_3{X}_3{X}_2{X}_1{X}_0$
• D. ${\overline{X}}_3{\overline{X}}_3{\overline{X}}_3{\overline{X}}_3{X}_3{X}_2{X}_1{X}_0$

Answer 1

The correct option is C $X_3{X}_3{X}_3{X}_3{X}_3{X}_2{X}_1{X}_0$

To extend number of bits in 1's compliment or 2's compliment copy MSB bit.
So, When the 4-bit number $X_3{X}_2{X}_1{X}_0$ is stored using 8-bit, MSB is copied. So, The required 8-bit number is $X_3{X}_3{X}_3{X}_3{X}_3{X}_2{X}_1{X}_0$.