The problem asks us to solve $A + B$ for the given two signed binary numbers and provide the result in decimal.

Given:

• $A = 1111011_2$
• $B = 1111101_2$

These are signed binary numbers (in two's complement form). Let's solve it step by step.

Step 1: Determine if the numbers are positive or negative

• In two's complement, if the leftmost bit (most significant bit) is 1, the number is negative.
• Both $A$ and $B$ start with $1$, so both are negative.

Step 2: Convert $A$ to decimal

1. Find the magnitude:

   • Invert all bits: $A = 1111011_2$ becomes $0000100_2$.
   • Add 1 to the result: $0000100_2 + 1 = 0000101_2$.
   • The magnitude is $5_{10}$.

2. Since $A$ is negative, $A = -5_{10}$.

Step 3: Convert $B$ to decimal

1. Find the magnitude:

   • Invert all bits: $B = 1111101_2$ becomes $0000010_2$.
   • Add 1 to the result: $0000010_2 + 1 = 0000011_2$.
   • The magnitude is $3_{10}$.

2. Since $B$ is negative, $B = -3_{10}$.

Step 4: Add $A$ and $B$

$A + B = -5 + (-3) = -8$

Final Answer:

$A + B = -8_{10}$

Let me know if you'd like a detailed explanation or have further questions! 😊

5 Related Questions:

1. How do you convert unsigned binary numbers to decimal?
2. What are the key differences between signed and unsigned binary representations?
3. How does the two's complement method handle subtraction of binary numbers?
4. How can you detect overflow in two's complement arithmetic?
5. What are the practical applications of signed binary numbers in computing?

Tip:

When working with two's complement numbers, always verify the sign (positive or negative) by checking the most significant bit first!