The 2's- complement system is to be used to add the signed binary numbers 11110010 and 11110011. Determine the sign and decimal value of each of these numbers and their sum.
A) - 113 and - 114, - 227
B) - 14 and - 13, - 27
C) - 11 and - 16, - 27
D) - 27 and - 13, - 40

Question

Quizplus · Accepted Answer

In the 2's-complement system, the leftmost bit indicates the sign (0 for positive, 1 for negative). To find the decimal value of a negative binary number in 2's-complement, invert all bits and add 1. For 11110010, inverting gives 00001101, adding 1 gives 00001110, which is 14 in decimal, so the original is -14. For 11110011, inverting gives 00001100, adding 1 gives 00001101, which is 13 in decimal, so the original is -13. Adding -14 and -13 gives -27.

The 2's- Complement System Is to Be Used to Add