Question

Which decimal number is represented as 1101011 in binary code?

OA. 143
OB. 99
C. 122
D. 107

Answer 1

Answer: 107 (choice D)

Work Shown

`\begin{array}c \cline{1-8}A & 1 & 1 & 0 & 1 & 0 & 1 & 1\\\cline{1-8}B & 64 & 32 & 16 & 8 & 4 & 2 & 1\\\cline{1-8}C & 64 & 32 & 0 & 8 & 0 & 2 & 1\\\cline{1-8}\end{array}`

Row A represents the digits of the given binary value.

Row B represents powers of 2 starting at 2^6 = 64, then we count down to 2^5 = 32, then 2^4 = 16, and so on until reaching 2^0 = 1. Always make sure that 2^0 = 1 is the right-most value.

Row C is the product of rows A and B.

Add up the items in row C to get: 64+32+0+8+0+2+1 = 107 which is the final answer.

Therefore, the binary number 1101011 converts to the decimal number 107.

1101011 base 2 = 107 base 10

We can write that as

`1101011_(2) = 107_(10)`