SIGNED BINARY NUMBERS

In signed binary numbers, the most significant bit (MSB) serves as the sign bit:

• 0 - Represents a positive number;
• 1 - Represents a negative number;

The relationship between a number and its negative counterpart is represented by the equation, which is a law in arithmetic, A + (−A) = 0.

Let’s do an example for negative numbers:

> 0 000 0000 = 0
> 1 000 0010 = -2
> 0 000 0010 = 2

  1 000 0010 (Represents -2)
+ 0 000 0010 (Represents 2)
------------
  1 000 0100 (Represents -4)

The unexpected result of -4 contradicts the arithmetic law A + (−A) = 0. Alongside utilizing the MSB sign bit to denote negative values, I employ two’s complement to accurately represent negative numbers in binary arithmetic.