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Convert Negative Decimal to Hexadecimal Calculator

Reviewed by Calculator Editorial Team

Converting negative decimal numbers to hexadecimal is a common task in programming and computer science. This guide explains the process, provides a calculator, and includes examples to help you understand how to perform these conversions accurately.

How to Convert Negative Decimal to Hexadecimal

Converting a negative decimal number to hexadecimal involves several steps. First, you need to understand the two's complement representation used in most computer systems. Here's a step-by-step process:

  1. Convert the absolute value of the decimal number to binary.
  2. Pad the binary number with leading zeros to make it a 32-bit or 64-bit number, depending on your system.
  3. Invert all the bits (change 0s to 1s and 1s to 0s).
  4. Add 1 to the inverted binary number.
  5. Convert the resulting binary number to hexadecimal.

Note: The exact number of bits used depends on the system architecture. For most modern systems, 32-bit or 64-bit representations are common.

Conversion Formula

The conversion process can be summarized with the following formula:

Hexadecimal = Two's Complement(Binary(Absolute Value(Decimal)))

Where Two's Complement is calculated as:

  1. Binary representation of the absolute value of the decimal number.
  2. Invert all bits.
  3. Add 1 to the inverted binary number.

Examples

Let's look at a few examples to understand the conversion process better.

Example 1: Convert -5 to Hexadecimal

  1. Absolute value: 5
  2. Binary of 5: 00000000 00000000 00000000 00000101
  3. Invert bits: 11111111 11111111 11111111 11111010
  4. Add 1: 11111111 11111111 11111111 11111011
  5. Hexadecimal: FFFFFFFB

Example 2: Convert -123 to Hexadecimal

  1. Absolute value: 123
  2. Binary of 123: 00000000 00000000 00000000 01111011
  3. Invert bits: 11111111 11111111 11111111 10000100
  4. Add 1: 11111111 11111111 11111111 10000101
  5. Hexadecimal: FFFFFFFD

FAQ

What is the difference between signed and unsigned hexadecimal?
Signed hexadecimal represents both positive and negative numbers using two's complement, while unsigned hexadecimal only represents positive numbers. The range of values they can represent is different.
Can I convert negative hexadecimal to decimal?
Yes, you can convert negative hexadecimal to decimal by first converting it to binary, then applying the two's complement process to get the absolute value, and finally converting that binary to decimal.
What is the range of negative numbers in 32-bit hexadecimal?
In 32-bit hexadecimal, the range of negative numbers is from -2,147,483,648 to -1, represented as 80000000 to FFFFFFFF.
Why do I need to invert the bits and add 1 for negative numbers?
This process is known as two's complement and is used to represent negative numbers in binary and hexadecimal. It allows for efficient arithmetic operations and maintains consistency with positive numbers.