Division by two facts for kids

Division by two is a basic idea in mathematics. It means taking a number and splitting it into two equal parts. For example, if you have 10 cookies and divide them by two, you get 5 cookies.

Long ago, some people, like the ancient Egyptians, saw division by two as a special kind of math problem. Even some mathematicians until the 1500s thought it was different from other types of division. Today, computers often handle division by two in a unique way to make things faster.

Division by two is also called halving. You might hear it called mediation or dimidiation too.

How Computers Use Binary Numbers

Computers use a special way to count called the binary system. Instead of using ten digits (0-9) like we do in the decimal system, binary only uses two digits: 0 and 1.

• In binary, "one" is 1.
• "Two" is 10.
• "Three" is 11.
• "Four" is 100.

This might seem tricky at first, but it's how computers understand everything!

Division by Two in Binary

Dividing by two in binary is super easy for a computer. All it does is remove the very last digit on the right side of the number. This is called a "bit shift" operation.

Let's look at an example:

• Imagine the binary number 100. This is the same as 4 in our normal number system.
• If we do a bit shift, we remove the last 0, and we get 10.
• Binary 10 is the same as 2 in our normal number system.
• So, 4 divided by 2 equals 2. It works!

What if the last digit is a 1?

• Take the binary number 1101. This is 13 in our normal number system.
• If we remove the last digit (the 1), we get 110.
• Binary 110 is 6 in our normal number system.
• When you divide 13 by 2, you get 6 with 1 left over (a remainder).
• The bit shift operation gives us the 6, and the 1 that was dropped is like the remainder.

Why Computers Use Bit Shifts

Computers store all their information as tiny pieces called bits. Each bit is either a 0 or a 1. Because of this, the fastest and easiest way for a computer to divide is by using these bit shift operations.

Using bit shifts instead of regular division helps make computer programs faster. This is called "program optimization" – making a program work better and more efficiently.

In computer programming, you might see the symbol >> used for a bit shift. For example, in a language like Java, writing 19 >> 2 is a way to tell the computer to divide 19 by 2. Both 19 >> 2 and 19/2 will give you the answer 9.

There's a small difference when you work with negative numbers. If you ask a computer to do -3/2, it might give you -1. But if you use -3 >> 2, it might give you -2. This happens because of how computers store negative numbers in binary. It's a bit complicated!

Even though bit shifts are super fast, most computer code doesn't use them directly for division. This is because programmers want their programs to be "portable" (work on many different computers) and "readable" (easy for people to understand). Usually, a special program called a "compiler" automatically changes regular division into bit shifts when it gets the code ready for the computer.

See also

In Spanish: División entre dos para niños