How Binary to Decimal Positional Conversion Works
Converting from binary (base 2) to decimal (base 10) relies on positional notation. Each bit column represents an ascending power of two, beginning with 2^0 = 1 on the far right, followed by 2^1 = 2, 2^2 = 4, 2^3 = 8, 2^4 = 16, and so forth.
The Positional Weight Formula
Decimal Value = (d_n * 2^n) + ... + (d_2 * 2^2) + (d_1 * 2^1) + (d_0 * 2^0)
Worked Conversion Example: 110101 in Binary
Bit 5 (2^5 = 32): 1 * 32 = 32
Bit 4 (2^4 = 16): 1 * 16 = 16
Bit 3 (2^3 = 8): 0 * 8 = 0
Bit 2 (2^2 = 4): 1 * 4 = 4
Bit 1 (2^1 = 2): 0 * 2 = 0
Bit 0 (2^0 = 1): 1 * 1 = 1
Total Decimal Sum: 32 + 16 + 0 + 4 + 0 + 1 = 53
Need to Convert in the Other Direction?
Decimal to Binary Convert standard decimal integers into base-2 binary strings.