Final answer:
In 8-bit signed magnitude arithmetic, the sum of the decimal numbers 13 and -19 is -6. This result is obtained by converting both numbers into binary form, performing binary subtraction, and then converting the result back to decimal form.
Step-by-step explanation:
To find the sum of the decimal numbers 13 and -19 using 8-bit signed magnitude arithmetic, first convert the numbers into their binary signed magnitude representations. The number 13 is represented as 00001101, where the first bit (0) represents a positive sign. The number -19, with the sign bit set to represent a negative value, is represented as 10010011.
Next, add the two numbers:
- 00001101 (13)
- 10010011 (-19)
However, since one of the numbers is negative, we must subtract the smaller number from the larger and give the result the sign of the larger number magnitude which is -19 in this case.
Performing the subtraction using binary arithmetic gives us:
- 10010011 (-19)
- 1111011 (inversion of 00001101, which is 13)
- +1 (adding 1 to the result of the inversion)
- -----------------
- 10001010 (Result in binary)
The binary result 10001010 represents the decimal number -6, since the most significant bit indicates a negative value.
Therefore, the sum of 13 and -19 using 8-bit signed magnitude arithmetic is -6.