question 1 (11 points) 5 minutes represent the following decimal (base - 10) number, - 107, in binary using…

Explanation:

Step1: Convert positive 107 to binary

First, find binary of 107. Divide 107 by 2 successively: $107\div2 = 53$ remainder $1$ $53\div2 = 26$ remainder $1$ $26\div2 = 13$ remainder $0$ $13\div2 = 6$ remainder $1$ $6\div2 = 3$ remainder $0$ $3\div2 = 1$ remainder $1$ $1\div2 = 0$ remainder $1$ Reading remainders from bottom - to - top, $107_{10}=1101011_2$.

Step2: 8 - bit signed magnitude

In 8 - bit signed magnitude, the left - most bit is the sign bit. For a negative number, the sign bit is 1. Pad the binary of 107 to 7 bits ($01101011$) and add a 1 as the sign bit. So, $- 107$ in 8 - bit signed magnitude is $11101011$.

Step3: 8 - bit one's complement

First, get the binary of positive 107 as $01101011$. Then, for one's complement of a negative number, flip all the bits. So, $01101011$ becomes $10010100$.

Step4: 8 - bit two's complement

Start with the one's complement $10010100$. Then, add 1 to it. $10010100+1 = 10010101$.

Answer:

A. $11101011$ B. $10010100$ C. $10010101$