Digital Logic | 2's complement Question | MadeEasy Workbook question

Question

Q. 13 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. $0000 X_{3} X_{2} X_{1} X_{0}$
  
• B. $1111 x_{3} x_{2} x_{1} x_{0}$
  
• C. $X_{3} x_{3} x_{3} X_{3} X_{3} x_{2} X_{1} x_{0}$
  
• D. $\bar{X}_{3} \bar{X}_{3} \bar{X}_{3} \bar{X}_{3} \bar{X}_{3} X_{2} X_{1} X_{0}$

Comments

option C is correct

copy the msb bit

---

Sign Extension in ALL Number Representations: https://youtu.be/dkoaDtyiz9k

Answer 1

A $4$ bit $2’s$ complement representation of a number is $X_3X_2X_1X_0$. To represent it in $8$ bit form just simply copy the sign bit for an extra bit that is :

$X_3X_2X_1X_0$ can be represent in $8$ bit form as: $X_3X_3X_3X_3X_3X_2X_1X_0$.

Option (A),(B) is wrong here it represents positive and negative numbers respectively.

Option (C) is correct.