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Convert Negative Decimal to Hex Calculator

Reviewed by Calculator Editorial Team

Converting negative decimal numbers to hexadecimal requires special handling due to the two's complement representation used in computing. This calculator provides an accurate conversion while explaining the underlying process.

How to Convert Negative Decimal to Hex

The process involves several steps to ensure accurate conversion of negative decimal numbers to hexadecimal:

  1. Identify the number of bits in the target representation (commonly 8, 16, 32, or 64 bits)
  2. Convert the absolute value of the decimal number to binary
  3. Pad the binary representation to the desired bit length
  4. Invert all bits (1's complement)
  5. Add 1 to the inverted bits (2's complement)
  6. Convert the final binary number to hexadecimal

Important Note

The bit length must be specified as it affects the range of representable negative numbers. Common choices are 8-bit (range -128 to 127), 16-bit (range -32,768 to 32,767), etc.

Conversion Formula

Two's Complement Conversion

For a negative decimal number D with bit length n:

  1. Compute the absolute value: |D|
  2. Convert |D| to binary
  3. Pad with leading zeros to make n bits
  4. Invert all bits (1's complement)
  5. Add 1 to the inverted bits (2's complement)
  6. Convert the final binary to hexadecimal

The result is the hexadecimal representation of the negative number in two's complement form.

Worked Examples

Example 1: Convert -5 to 8-bit Hex

  1. Absolute value: 5
  2. Binary of 5: 101
  3. Pad to 8 bits: 00000101
  4. Invert bits: 11111010
  5. Add 1: 11111011
  6. Hexadecimal: FB

The hexadecimal representation of -5 in 8-bit two's complement is FB.

Example 2: Convert -256 to 16-bit Hex

  1. Absolute value: 256
  2. Binary of 256: 100000000
  3. Pad to 16 bits: 00000000100000000
  4. Invert bits: 11111111011111111
  5. Add 1: 11111111100000000
  6. Hexadecimal: FF00

The hexadecimal representation of -256 in 16-bit two's complement is FF00.

FAQ

Why can't I just convert the negative decimal directly to hex?
Hexadecimal is a base-16 representation that doesn't natively support negative numbers. The two's complement method is used to represent negative numbers in binary, which can then be converted to hexadecimal.
What happens if the number is too large for the specified bit length?
The conversion will produce incorrect results. The bit length must be chosen to accommodate the magnitude of the negative number.
Can I convert hexadecimal back to negative decimal?
Yes, you can reverse the process by converting the hexadecimal to binary, then applying the two's complement conversion to get the negative decimal value.
What are common bit lengths used in computing?
Common bit lengths are 8-bit (bytes), 16-bit (words), 32-bit (dwords), and 64-bit (qwords). The choice depends on the system architecture.
Is there a difference between signed and unsigned hexadecimal?
Yes, signed hexadecimal represents negative numbers using two's complement, while unsigned hexadecimal represents only positive values. The interpretation depends on the context.