Power of two facts for kids

In mathematics, a power of two is a number you get by multiplying the number two by itself a certain number of times. For example, 2 multiplied by itself once is 2 (2¹), twice is 4 (2²), three times is 8 (2³), and so on.

These numbers are super important in binary code, which computers use. Think of them like powers of ten (like 10, 100, 1000) are for our everyday decimal system. Numbers that are one less than a power of two are called Mersenne numbers. Some of these are special prime numbers!

This picture shows powers of two from 1 (which is 2⁰) all the way up to 1024 (which is 2¹⁰).

What are Powers of Two?

A power of two is simply the number 2 raised to an integer power. This means you take the number 2 and multiply it by itself a certain number of times. The "power" tells you how many times to multiply it.

For example:

• 2⁰ = 1 (Any number to the power of zero is 1)
• 2¹ = 2 (2 multiplied by itself 1 time)
• 2² = 2 × 2 = 4 (2 multiplied by itself 2 times)
• 2³ = 2 × 2 × 2 = 8 (2 multiplied by itself 3 times)
• 2⁴ = 2 × 2 × 2 × 2 = 16 (2 multiplied by itself 4 times)

You can see that each number in the sequence is double the one before it.

Why are They Important?

Powers of two are everywhere in the world of computers and technology. This is because computers use a binary system, which only has two digits: 0 and 1.

How Computers Use Powers of Two

Every piece of information in a computer, from a picture to a game, is stored using these 0s and 1s. Each 0 or 1 is called a "bit." When you group bits together, they can represent larger numbers.

• 1 bit can represent 2 values (0 or 1).
• 2 bits can represent 4 values (00, 01, 10, 11).
• 3 bits can represent 8 values (000, 001, 010, 011, 100, 101, 110, 111).

Notice a pattern? The number of values you can represent is always a power of two!

• 2 values = 2¹
• 4 values = 2²
• 8 values = 2³

This is why computer memory (like RAM) and storage (like hard drives) often come in sizes that are powers of two, such as 512 MB, 1 GB (1024 MB), 2 GB, 4 GB, 8 GB, 16 GB, and so on.

Powers of Two in Daily Tech

You might see powers of two in other places too:

• Screen Resolutions: The number of pixels on your computer screen or phone often uses numbers related to powers of two, like 1920x1080 (which is not a direct power of two, but the total number of pixels might be close to one, or the underlying memory addressing uses powers of two).
• Data Transfer Speeds: Network speeds, like 100 Mbps or 1 Gbps, are often based on powers of two for efficient data handling.
• Computer Graphics: Textures and other elements in video games often have dimensions that are powers of two (e.g., 256x256 pixels) because it makes them easier for the computer to process.

Mersenne Numbers

A Mersenne number is a number that is one less than a power of two. They are written in the form 2ⁿ - 1.

For example:

• 2² - 1 = 4 - 1 = 3
• 2³ - 1 = 8 - 1 = 7
• 2⁴ - 1 = 16 - 1 = 15

Some Mersenne numbers are also prime numbers. These are called Mersenne primes. Finding new Mersenne primes is a big deal in mathematics, and they are often the largest known prime numbers!

See also

In Spanish: Potencia de dos para niños