The following numbers are in 8-bit, two's complement notation.
Find the decimal equivalent for each.
-$$11110001 _ { 2 ^ { * } }$$
A) 15
B) 242
C) −15
D) −242
E) None of these

Question

Quizplus · Accepted Answer

In two's complement notation, the leftmost bit indicates the sign of the number (0 for positive, 1 for negative). To find the decimal equivalent of a negative number in two's complement, first invert all the bits and then add 1. For $11110001_2$, inverting gives $00001110_2$, and adding 1 gives $00001111_2$, which is 15 in decimal. Since the original number was negative, its decimal equivalent is $-15$.

The Following Numbers Are in 8-Bit, Two's Complement Notation 111100012∗11110001 _ { 2 ^ { * } }111100012∗​

The Following Numbers Are in 8-Bit, Two's Complement Notation $11110001 _ { 2 ^ { * } }$