Signed Binary Numbers

Perform the arithmetic addition of the two decimal numbers given in List-I using the signed-complement system. Match the corresponding output of List-I with binary number representation given in List-II.
$%5Cbegin%7Barray%7D%7B%7Cc%7Cc%7C%7D%5Chline%20%5Ctext%7BList-I%7D%20%26%20%5Ctext%7BList-II%7D%20%5C%5C%20%5Chline%20%5Ctext%7B(A)%20%2B6%2C%20%2B13%7D%20%26%20%5Ctext%7B(I)%2000000111%7D%20%5C%5C%20%5Chline%20%5Ctext%7B(B)%20-6%2C%20%2B13%7D%20%26%20%5Ctext%7B(II)%2000010011%7D%20%5C%5C%20%5Chline%20%5Ctext%7B(C)%20%2B6%2C%20-13%7D%20%26%20%5Ctext%7B(III)%2011101011%7D%20%5C%5C%20%5Chline%20%5Ctext%7B(D)%20%2B6%2C%20-13%7D%20%26%20%5Ctext%7B(IV)%2011111101%7D%20%5C%5C%20%5Chline%20%5Cend%7Barray%7D$

Step 1: Converting Decimal Numbers to Signed Binary.
- For **+6** and **+13**, we convert them to signed 8-bit binary: - $%2B6%20%3D%2000000110_2$ - $%2B13%20%3D%2000001101_2$ - For **-6** and **+13**, we convert them using two's complement: - $-6%20%3D%2011111010_2$ - $%2B13%20%3D%2000001101_2$ - For **+6** and **-13**, we convert **-13** using two's complement: - $%2B6%20%3D%2000000110_2$ - $-13%20%3D%2011110011_2$ - For **-6** and **-13**, we convert both using two's complement: - $-6%20%3D%2011111010_2$ - $-13%20%3D%2011110011_2$

Step 2: Conclusion.
The correct mapping is: - (A) +6, +13 → **(I)** 00000111 - (B) -6, +13 → **(II)** 00001011 - (C) +6, -13 → **(III)** 11110101 - (D) -6, -13 → **(IV)** 11111100

High-Yield Trend

Chapter Questions
1 MCQs

Official Solution

Signed Binary Numbers

High-Yield Trend

Chapter Questions 1 MCQs

Official Solution

Chapter Questions
1 MCQs