Question

Two's Complement binary addition and subtraction Calculate the sum of the given 8-bit Two's Complement binary numbers. All calculations must be done using Two's Complement binary arithmetic. Show your work. Specify each result as an 8-bit Two's Complement binary number. Indicate if overflow occurred.

01001110
+01100011

Answer 1

In Two's Complement binary arithmetic, positive numbers are represented as is, while negative numbers are represented by first taking the complement of the positive number and then adding 1. To calculate the sum of two Two's Complement binary numbers, add them as if they were unsigned binary numbers, and discard any carry out of the MSB.

Step-by-step explanation:

In Two's Complement binary arithmetic, positive numbers are represented as is, while negative numbers are represented by first taking the complement of the positive number and then adding 1. To calculate the sum of two Two's Complement binary numbers, add them as if they were unsigned binary numbers, and discard any carry out of the most significant bit (MSB). If the sum is negative (MSB is 1), take the Two's Complement of the sum to get the final result.

In this case, we have:

1. Convert 01001110 and 01100011 to decimal: 01001110 = 78 and 01100011 = 99
2. Add the decimal numbers: 78 + 99 = 177
3. Convert the result back to an 8-bit Two's Complement binary number: 177 = 10110001
4. Since the MSB of the sum is 1, the final result is -78. Overflow occurred because the sum cannot be represented in an 8-bit Two's Complement binary number.