Binary to Decimal Conversion

In this post we will cover how to convert binary number to decimal number. For decimal to binary conversion refer - Binary to Decimal Number Conversion.

Formula

Here is the formula:

Decimal number = ∑( Ni * (Base ^ Position) )

• ∑ represents the summation
• ^ denotes exponentiation (power)
• * denotes multiplication

and

• Ni: Each digit of the number
• Base: The base value of the number system
• Position: The position of each digit, starting from 0 on the right

Understanding Base Values

Here are base values of different number system:

Understanding Position

• Position starts at 0 from the rightmost digit to (number of digits - 1)
• For a two-digit number, positions are 0 and 1.
• For a three-digit number, positions are 0, 1, and 2.

Example

Let’s convert (10110)₂ into the decimal number:

• Assign positions from right to left:
  • The digit 0 has position 0
  • The digit 1 has position 1
  • The digit 1 has position 2
  • The digit 0 has position 3
  • The digit 1 has position 4
• The base value (for binary) is 2

Using the formula: = (10110)₂ = 1*(2⁴) + 0*(2³) + 1*(2²) + 1*(2¹) + 0*(2⁰) = 16 + 0 + 4 + 2 + 0 = (22)₁₀

Pictorial Explanation