Chapter 16, Problem 1R

To determine

To calculate: The decimal representation of the provided binary number $1101$.

Answer to Problem 1R

Solution:

The decimal representation of the provided binary number is $13$.

Explanation of Solution

Given Information:

The provided binary number is $1101$.

Formula used:

To convert a binary number to a decimal number, write down the powers of two from right to left and add. Start at $2^0$ and increment the exponent by one of each power.

Calculation:

Consider the provided binary number,

$1101$

Now, the equivalent decimal notation for the above binary number will be obtained by writing down the powers of two from right to left and adding them as,

$\begin{array}{c}1101=1\times 2^3+1\times 2^2+0\times 2^1+1\times 2^0\\ =8+4+0+1\\ ={13}_{10}\end{array}$

Thus, the decimal representation of the provided binary number is $13$.