Final answer:
In 8-bit signed magnitude arithmetic, the sum of 13 and -19 is represented as -6, because after converting to binary, performing the subtraction of their magnitudes, and assigning the sign of the larger absolute value, we get a final result of 10000110 in binary, which corresponds to -6 in decimal form.
Step-by-step explanation:
Using 8-bit signed magnitude arithmetic, we can represent the decimal numbers 13 and -19 as follows:
- 13 in binary: 00001101
- -19 in binary: 10010011 (most significant bit indicates the sign)
When performing addition, we follow the rule that when two numbers having opposite signs add, we subtract the smaller number from the larger number, and the answer has the sign of the larger number. However, because we are working with signed magnitude representation, we must first convert them into their absolute values, perform the subtraction, and then apply the sign of the larger number.
The absolute values of 13 and 19 in binary are 00001101 and 00010011, respectively. Subtracting 13 from 19, we get 6. The binary representation of 6 is 00000110. Since -19 has a larger absolute value than +13, the result will be negative: 10000110, which corresponds to -6 in decimal form.