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Convert Negative Binary to Decimal Calculator

Reviewed by Calculator Editorial Team

This calculator converts negative binary numbers to their decimal equivalents. Binary numbers are fundamental in computer science, and understanding how negative binary works is essential for programming and digital systems.

How to Convert Negative Binary to Decimal

Negative binary numbers are represented using two's complement, a common method in computing. Here's how the conversion works:

  1. Identify the number of bits in the binary number.
  2. If the leftmost bit is 1, the number is negative.
  3. To convert to decimal, invert all bits, add 1, then treat the result as a positive binary number.
  4. Convert the resulting positive binary number to decimal.

For example, converting -1 in 4-bit binary:

  • Binary: 1111 (negative)
  • Invert: 0000
  • Add 1: 0001
  • Decimal: 1

The Formula

For a negative n-bit binary number:

  1. Invert all bits: 1 becomes 0, 0 becomes 1
  2. Add 1 to the inverted number
  3. Convert the result to decimal using standard binary-to-decimal conversion
  4. Apply negative sign to the decimal result

This method ensures proper representation of negative numbers in binary systems.

Worked Examples

Example 1: 4-bit -2

Binary: 1110

  1. Invert: 0001
  2. Add 1: 0010
  3. Decimal: 2
  4. Final result: -2

Example 2: 8-bit -128

Binary: 10000000

  1. Invert: 01111111
  2. Add 1: 10000000
  3. Decimal: 128
  4. Final result: -128

FAQ

What is two's complement?
Two's complement is a method for representing negative numbers in binary. It's widely used in computing because it simplifies arithmetic operations.
Why do we invert and add 1?
Inverting the bits and adding 1 is a mathematical operation that converts a negative binary number to its positive equivalent, which can then be converted to decimal.
Can this method be used for floating-point numbers?
No, this method is specifically for integer values in two's complement representation. Floating-point numbers use a different encoding system.
What's the largest negative number that can be represented in n bits?
The largest negative number in n bits is -2^(n-1). For example, in 8 bits it's -128.