Binary to Decimal Converter

Table of Contents

• How does binary to decimal conversion work?
• Binary to decimal conversion formula
• Conversion process
• Example #1
• Example #2
• Binary to decimal conversion table

How does binary to decimal conversion work?

Binary to decimal conversion involves interpreting the value of a binary number (composed only of zeros and ones) as a decimal number. The binary system is base 2, while the decimal system is base 10. To perform this conversion, each digit in the binary number is multiplied by a power of 2, starting from the right (power zero) to the left.

Binary to decimal conversion formula

For a binary number with n digits, the formula for conversion to decimal is:

where b_n represents each binary digit (0 or 1) at position n.

Conversion process

1. Write down the binary number and assign powers of 2 to each digit, starting with 2⁰ from the right.
2. Multiply each binary digit by its respective power of 2.
3. Add all the multiplication results to obtain the decimal value.

Example #1

Convert the binary number 1011 to decimal:

1. Assign the powers:

   (1 × 23), (0 × 22), (1 × 21), (1 × 20)

2. Multiplications:

   (1 × 8) = 8, (0 × 4) = 0, (1 × 2) = 2, (1 × 1) = 1

3. Addition:

   8 + 0 + 2 + 1 = 11

Result: 1011 in binary is 11 in decimal.

Example #2

Convert the binary number 11010 to decimal:

1. Assign the powers:

   (1 × 24), (1 × 23), (0 × 22), (1 × 21), (0 × 20)

2. Multiplications:

   (1 × 16) = 16, (1 × 8) = 8, (0 × 4) = 0, (1 × 2) = 2, (0 × 1) = 0

3. Addition:

   16 + 8 + 0 + 2 + 0 = 26

Result: 11010 in binary is 26 in decimal.

Binary to decimal conversion table