Bit to Decimal Calculator with Steps and Binary Explanation

Formula Used: How Bits Convert to Decimal

For an unsigned binary number with bits b_{n-1} b_{n-2} ... b_{1} b_{0}, the decimal value is:

decimal = b_{n-1} × 2^{n-1} + b_{n-2} × 2^{n-2} + ... + b_{1} × 2^{1} + b_{0} × 2^{0}

For signed two's complement with n bits, the decimal value is: decimal = -b_{n-1} × 2^{n-1} + ∑ (b_i × 2^i) for i = 0 to n-2.

How to Use This Bit to Decimal Calculator

1. Enter a binary sequence in the main input field.
2. Select whether to treat it as unsigned or signed (two's complement).
3. Click Convert Bit to Decimal to see the decimal value and steps.
4. For multiple values, paste one binary number per line in the bulk area.
5. Review the Conversion History and export it as CSV or PDF when needed.

This tool is ideal for debugging, teaching, preparing documentation, or verifying low-level data representations.

Example: Using the Bit to Decimal Calculator

Imagine you want to convert the binary value 11010110.

1. Enter 11010110 in the main input field.
2. Select Unsigned (pure binary to decimal) mode.
3. Click Convert Bit to Decimal.
4. The calculator shows: 1×2^7 + 1×2^6 + 0×2^5 + 1×2^4 + 0×2^3 + 1×2^2 + 1×2^1 + 0×2^0 = 128 + 64 + 16 + 4 + 2 = 214.
5. Switch to Signed (two's complement) mode with 8 bits to see it interpreted as a negative number: -42.

This demonstrates how the same bits can represent different values depending on unsigned or signed interpretation.

Understanding Bit Positions and Positional Weights

Each bit represents a power of two, starting from 2^0 on the right. The calculator multiplies every 1-bit by its weight and sums contributions to generate the corresponding decimal result precisely.

Common Bit-Length Ranges and Limits

For 8 bits, unsigned values range from 0 to 255, signed from -128 to 127. For 16 bits, unsigned spans 0 to 65535, signed from -32768 to 32767.

Practical Uses of Bit to Decimal Conversion

Use this tool when decoding binary flags, parsing communication protocols, inspecting microcontroller registers, evaluating masks, or teaching students how digital systems map bit patterns to human-readable numeric values.