Binary to Decimal Converter Formula

Understand the math behind the binary to decimal converter. Each variable explained with a worked example.

Use the Binary to Decimal Converter

Formulas Used

Decimal Value

decimal = bit7 * 128 + bit6 * 64 + bit5 * 32 + bit4 * 16 + bit3 * 8 + bit2 * 4 + bit1 * 2 + bit0 * 1

Variables

VariableDescriptionDefault
bit7Bit 7 (128s)0
bit6Bit 6 (64s)0
bit5Bit 5 (32s)0
bit4Bit 4 (16s)1
bit3Bit 3 (8s)0
bit2Bit 2 (4s)1
bit1Bit 1 (2s)0
bit0Bit 0 (1s)1

How It Works

Binary to Decimal Converter

How It Works

Each binary digit (bit) represents a power of 2. From right to left:

  • Bit 0 = 2^0 = 1
  • Bit 1 = 2^1 = 2
  • Bit 2 = 2^2 = 4
  • Bit 3 = 2^3 = 8
  • Bit 4 = 2^4 = 16
  • Bit 5 = 2^5 = 32
  • Bit 6 = 2^6 = 64
  • Bit 7 = 2^7 = 128

    • Multiply each bit by its place value and sum all the results.

    Worked Example

    Convert binary 00010101 to decimal.

    bit7 = 0bit6 = 0bit5 = 0bit4 = 1bit3 = 0bit2 = 1bit1 = 0bit0 = 1
    1. 010×128 + 0×64 + 0×32 + 1×16 + 0×8 + 1×4 + 0×2 + 1×1
    2. 02= 0 + 0 + 0 + 16 + 0 + 4 + 0 + 1
    3. 03= 21 in decimal

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