Each of the following numbers are in 8-bit, two's complement notation. Translate each into its decimal equivalent.
-$10110101 _ { 2 } *$
A) −75
B) 75
C) −181
D) 181
E) None of these

Question

Quizplus · Accepted Answer

In two's complement notation, the leftmost bit indicates the sign of the number. If the leftmost bit is 1, the number is negative. To find the decimal equivalent of a negative number in two's complement, first invert all the bits and then add 1. For $10110101_2$, inverting all bits gives $01001010_2$, and adding 1 gives $01001011_2$, which is $75_{10}$ in decimal. Since the original number was negative, its decimal equivalent is $-75$.

Each of the Following Numbers Are in 8-Bit, Two's Complement 101101012∗10110101 _ { 2 } *101101012​∗

Each of the Following Numbers Are in 8-Bit, Two's Complement $10110101 _ { 2 } *$