Negative numbers in Binary

To represent numbers, computers use either:

• Unsigned numbers
  Include only non-negative values (0 and positive numbers)

• Signed numbers
  Include positive and negative values

To represent negative numbers, computers use a technique called Two’s Complement.

In Two’s Complement, a negative number is created by inverting all the bits of the positive number and adding 1. The most significant bit (MSB) is used to indicate the sign. If it’s 0, the number is positive, and if it’s 1, the number is negative.

This is also why unsigned numbers can go to higher ranges. They don’t use the MSB as a sign bit, so they have one more bit available for the value.

Now, let’s look at an example of converting a number 5 to -5 using 8-bit binary.

The number 5 looks like this in 8 bits:

00000101

To get its negative, we first invert all of the bits:

~ 00000101
----------
  11111010

Then, we add 1 to it:

  11111010
+ 00000001
----------
  11111011

This gives us -5 in Two’s Complement.

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