What is Binary?

Binary is the language of computers that uses only two digits 0 and 1.

What is Decimal?

Decimal is our everyday numbers. It uses ten digits 0 to 9.

How to Convert Binary to Decimal

Each digit in a binary number stands for a power of 2. From right to left, the powers are 2^0, 2^1, 2^2, 2^3, and so on.

Small Example: Convert 1011 to Decimal

  1. Write out the binary number: 1011
  2. List the powers of 2:
    • Rightmost 1: 2^0 = 1
    • Second 1: 2^1 = 2
    • 0: 2^2 = 4 (but we ignore this because the digit is 0)
    • Leftmost 1: 2^3 = 8
  3. Add up the values where there's a 1: 8 + 2 + 1 = 11

So, 1011 in binary equals 11 in decimal.

Another Example: 10110

10110 = 16 + 0 + 4 + 2 + 0 = 22 in decimal

Conversion Table

Binary Decimal Explanation
0000 0 No bits set
0001 1 2^0 = 1
0010 2 2^1 = 2
0011 3 2^1 + 2^0 = 2 + 1
0100 4 2^2 = 4
0101 5 2^2 + 2^0 = 4 + 1
0110 6 2^2 + 2^1 = 4 + 2
0111 7 2^2 + 2^1 + 2^0 = 4 + 2 + 1
1000 8 2^3 = 8
1001 9 2^3 + 2^0 = 8 + 1
1010 10 2^3 + 2^1 = 8 + 2
1011 11 2^3 + 2^1 + 2^0 = 8 + 2 + 1
1100 12 2^3 + 2^2 = 8 + 4
1101 13 2^3 + 2^2 + 2^0 = 8 + 4 + 1
1110 14 2^3 + 2^2 + 2^1 = 8 + 4 + 2
1111 15 2^3 + 2^2 + 2^1 + 2^0 = 8 + 4 + 2 + 1