Chapter B, Problem 1E

To determine

To convert: The binary number ${100}_2$ to its equivalent decimal number.

Answer to Problem 1E

The equivalent decimal number form of the binary number ${100}_2$ is $\underset{\_}{4}$.

Explanation of Solution

Procedure used:

To convert a binary number to a decimal number:

1. Write the binary number in expanded form using the powers of 2.

2. Evaluate the powers of 2 in base 10 notation.

3. Perform the multiplication.

4. Perform the additions.

Calculation:

Obtain the expanded form of the binary number ${100}_2$.

$\begin{array}{c}{100}_2=1{\left(2\right)}^2+0{\left(2\right)}^1+0{\left(2\right)}^0\\ =1\left(4\right)+0\left(2\right)+0\left(1\right)\left[\text{Evaluate the powers}\right]\\ =4+0+0\left[\text{Multiply}\right]\\ =4\left[\text{Add}\right]\end{array}$

Thus, the equivalent decimal number form of the binary number ${100}_2$ is $\underset{\_}{4}$.