Convert binary numbers to decimal with a step-by-step positional breakdown showing each bit value and running total.
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Number Systems
The binary to decimal converter translates binary (base-2) numbers into their decimal (base-10) equivalents. Enter a binary string and see the decimal result with a positional breakdown of each bit.
Each binary digit represents a power of 2, starting from 2 to the power 0 on the right. Multiply each bit by its positional value and sum all the products to get the decimal result.
For example, binary 1101 equals 1 times 8 plus 1 times 4 plus 0 times 2 plus 1 times 1, which gives decimal 13.
decimal = sum of (bit_i * 2^i)
Each bit is multiplied by 2 raised to its position index, starting from 0 on the right.
Reading binary sensor data, interpreting register values, understanding subnet masks, and converting between machine-level representation and human-readable numbers all rely on binary-to-decimal conversion.
Frequently asked questions
Leading zeros do not change the decimal value. 00001101 and 1101 both equal 13 in decimal.
There is no mathematical limit. Practically, the calculator handles values within the range of standard number precision.
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