The following numbers are in 8-bit, two's complement notation.
Find the decimal equivalent for each.
-$$10000001 _ { 2 ^ { * } }$$
A) 130
B) −127
C) 127
D) −130
E) None of these

Question

Quizplus · Accepted Answer

In two's complement notation, the leftmost bit indicates the sign of the number, with 1 for negative numbers and 0 for positive numbers. To find the decimal equivalent of a negative number in two's complement, we invert all the bits and add 1. For the given number $10000001_2$, inverting all bits gives $01111110_2$, and adding 1 gives $01111111_2$, which is 127 in decimal. Since the original number was negative, its decimal equivalent is $-127$.

The Following Numbers Are in 8-Bit, Two's Complement Notation 100000012∗10000001 _ { 2 ^ { * } }100000012∗​

The Following Numbers Are in 8-Bit, Two's Complement Notation $10000001 _ { 2 ^ { * } }$