Signed number representations facts for kids

Computers use a special way to understand and store negative numbers. When computers work with numbers, they use a system called binary, which only uses 0s and 1s. The challenge is how to show if a number is positive or negative, because there isn't a special "minus" button or symbol in binary. If a computer just used a 0 for minus and a 1 for plus, it would get confused. It wouldn't know if that 0 or 1 was part of the number itself or meant it was positive or negative.

To solve this, computer experts came up with different ways to represent negative numbers in binary. The two main methods are called sign-and-magnitude and 2's complement. These methods help computers know if a number is positive or negative.

Sign-and-magnitude: The Simple Way

The Sign-and-magnitude method is one way to show negative numbers. It uses the very first digit (called the Most Significant Bit or MSB) to tell if a number is positive or negative.

• If the first digit is a 0, the number is positive.
• If the first digit is a 1, the number is negative.

Let's look at an example:

• `0000 0010` means the number 2 (positive).
• To make it -2 using sign-and-magnitude, the first digit changes to 1: `1000 0010` means -2.

However, this method has some problems:

• It makes math with binary numbers tricky for computers.
• Computers would need to know which method was used to store the number, which can be complicated.

1's Complement: Flipping Bits

1's Complement is another way to represent negative numbers. It works by "flipping" all the bits in a binary number. This means every 1 becomes a 0, and every 0 becomes a 1.

For example, to find -2 using 1's complement:

• Start with 2 in binary: `0000 0010`
• Flip all the bits: `1111 1101` (This is -2 in 1's complement).

Just like sign-and-magnitude, a number in 1's complement is easy to spot as negative because its first digit (MSB) is a 1.

2's Complement: The Most Common Way

2's Complement is a more popular and useful method for storing negative numbers in computers. It involves three steps:

1. Find the positive binary number. For example, the number 8 in regular binary is `0000 1000`.
2. Flip the bits: Change all the 1s to 0s and all the 0s to 1s. This is like the 1's complement step. So, `0000 1000` becomes `1111 0111`.
3. Add 1: Add 1 to the flipped number. So, `1111 0111` + `1` equals `1111 1000`. This is -8 in 2's complement.

Computers like the 2's complement method for a few reasons:

• It's easy to tell if a number is negative or positive: negative numbers start with a 1, and positive numbers start with a 0.
• It makes binary math much simpler and more accurate for computers.
• The number 0 only has one way to be represented (`0000 0000`), which avoids confusion.

See also

In Spanish: Representación de números con signo para niños