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_val = b7*128 + b6*64 + b5*32 + b4*16 + b3*8 + b2*4 + b1*2 + b0*1

Variables

VariableDescriptionDefault
b7Bit 7 (128s)0
b6Bit 6 (64s)0
b5Bit 5 (32s)0
b4Bit 4 (16s)0
b3Bit 3 (8s)1
b2Bit 2 (4s)0
b1Bit 1 (2s)1
b0Bit 0 (1s)0

How It Works

How to Convert Binary to Decimal

Method

Each position in a binary number represents a power of 2, starting from 2^0 on the right.

Decimal = b7×128 + b6×64 + b5×32 + b4×16 + b3×8 + b2×4 + b1×2 + b0×1

For example, binary 00001010:

  • Position 3 (8s place): 1 × 8 = 8
  • Position 1 (2s place): 1 × 2 = 2
  • Total: 8 + 2 = 10

    • Worked Example

    Convert binary 00001010 to decimal.

    b7 = 0b6 = 0b5 = 0b4 = 0b3 = 1b2 = 0b1 = 1b0 = 0
    1. 010×128 + 0×64 + 0×32 + 0×16 + 1×8 + 0×4 + 1×2 + 0×1
    2. 02= 0 + 0 + 0 + 0 + 8 + 0 + 2 + 0
    3. 03= 10

    Frequently Asked Questions

    What is the binary number system?

    Binary (base-2) uses only two digits: 0 and 1. It is the fundamental number system used by computers and digital electronics.

    Why do computers use binary?

    Computers use binary because electronic circuits have two stable states (on/off, high/low voltage), making base-2 the natural representation for digital data.

    How do you count in binary?

    0, 1, 10, 11, 100, 101, 110, 111, 1000... Each position doubles in value from right to left (1, 2, 4, 8, 16, 32, 64, 128, ...).

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