Binary to Decimal Formula
The binary to the decimal formula is used to convert the binary numbers into decimal numbers. The place value of each binary digit is important in accordance to convert it into a decimal number. Let us learn more about binary to decimal formula and conversion in the following section along with a few solved examples.
Formula to Convert Binary to Decimal
If individual binary digits are written as \(d_n\) where n is the position of the digit from the right end and n is a whole number starting from 0. Then, the binary to decimal formula is given as,
\(d_0 \times 2^0 + d_1 \times 2^1 + d_2 \times 2^2 + d_3 \times 2^3 ...\)
Let us have a look at a few solved examples to understand the binary to decimal formula better.
Solved Examples on Binary to Decimal Formula

Example 1: Using binary to decimal formula, find the decimal value of 111001_{2}.
Solution:
Using the binary to decimal formula of conversion,
\(d_0 \times 2^0 + d_1 \times 2^1 + d_2 \times 2^2 + d_3 \times 2^3 ...\)
\(111001_2 = 1 \times 2^0 + 1 \times 2^1 + 1 \times 2^2 + 0 \times 2^3 + 0 \times 2^4 + 1 \times 2^5 = 57_{10}\)Answer: Hence \(111001_2\)_{ }= \(57_{10}\)

Example 2: Find the decimal value of 100011_{2}.
Solution:
Using the binary to decimal formula of conversion:
\(d_0 \times 2^0 + d_1 \times 2^1 + d_2 \times 2^2 + d_3 \times 2^3 ...\)
\(100011_2 = 1 \times 2^0 + 1 \times 2^1 + 0 \times 2^2 + 0 \times 2^3 + 0 \times 2^4 + 1 \times 2^5 = 35_{10}\)Answer: Hence \(100011_2 = 35_{10}\)