# Byte Converter

Created by Davide Borchia
Last updated: Dec 16, 2022

Data storage is a rather young issue, of ever-increasing importance in the modern world: with our byte converter, you will learn how we measure data storage, and how to convert between the most common units.

• What is computer memory;
• What is a bit, and why it is so important;
• The multiples of the bit: how to convert the bit from decimal to binary multiples and vice versa;
• What is a byte;
• The multiples of the byte, and how to calculate the bytes in storage.

If you're already satisfied with our byte converter, then you can visit the other tool that quickly finds what day of the week is it based on the specific date you provide.

## What is a bit? The smallest unit of information

What's the smallest thing a human can remember? That's a good question, but it's easier to answer when we talk about computers.

Generally speaking, the smallest thing a computer can memorize is a single binary digit: a bit. A bit has either value $0$ or $1$. Bits represent binary logical states. Apart from $0$ and $1$, we can use them to represent other quantities, such as:

• True and False;
• On and Off;
• $+$ and $-$.

## The diverging ways of information: the multiples of the bit

Information can either move or get stored somewhere, even on your computer. The first situation usually refers to data transfer and transmission, while the other refers to data storage: their scopes are fairly different. Let's analyze them in detail.

The speed at which information is transferred from one place to another is measured in bits per second. Since this quantity is not easily controlled by the architecture of the device, computer scientists use a metric approach. The multiples of the bit per second are powers of $10$.

The amount of information that we can transfer in a second is then:

• A kilobit: $1\ \text{kbit} = 10^3\ \text{bit} = 1000\ \text{bit}$;
• A megabit: $1\ \text{Mbit} = 10^6\ \text{bit}$;
• A gigabit: $1\ \text{Gbit} = 10^9\ \text{bit}$;
• A terabit: $1\ \text{Tbit} = 10^{12}\ \text{bit}$.

The list goes on; however, your internet connection will rarely be higher than a few gigabits per second. The following multiples are the petabit, the exabit, the zettabit, and the yottabit.

Check our transfer speed calculator in case you want to transfer data between two different devices.

🙋 Researchers in Japan broke the world record for the fastest internet speed with $319\ \text{Tbit}/\text{s}$. A speed of one petabit per second was recorded during an experiment, but without practical applications.

#### Memory storage: why 1024?

As you've seen, computers are closely related to the number $2$. To measure the memory of a device, we need to take this into account. Imagine having a device able to store a single bit of memory (a flip-flop, maybe): it can save two states. Now pair it with a copy of itself: we can memorize four states.

What about three flip-flops? The answer is that we can store $2^3 = 8$.

This is a core concept in computer architecture: the memory scales with powers of 2, and not of 10. To take into account this different base, we need to introduce binary prefixes. Let's discover them while analyzing the storage multiples of the bit.

• The kibibit: $1\ \text{Kibit} = 2^{10}\ \text{bit} = 1024\ \text{bit}$;
• The mebibit: $1\ \text{Mibit} = 1024^2\ \text{bit}$;
• The gibibit: $1\ \text{Gibit} =1024^3\ \text{bit}$;
• The tebibit: $1\ \text{Tibit} = 1024^4\ \text{bit}$;

Of course we can go on with the pebibit ($\text{Pibit}$, exbibit ($\text{Eibit}$), etc.

Similarly to bytes, power units might also be confusing. For that reason, we prepared the power converter, which includes various popular power units.

## How to convert bits from decimal to binary and vice versa

To convert a bit multiple into another, multiply the quantity by the ratios defining the multiple itsef. Check this example: if you want to know how many gigabits is a gibibit (from binary to decimal), apply the following transformation:

$1\ \text{Gibit} \cdot \frac{1024^3\ \text{bit}}{1\ \text{Gibit}}\cdot\frac{1\ \text{Gbit}}{10^9\ \text{bit}}$

Which tells us that, approximately, $1\ \text{Gibit} = 1.074\ \text{Gbit}$. Apply this strategy to any other conversion you may need.

## Another one bytes the dust: 8 bits at a time

A bit stores very little memory, and from the dawn of computation, scientists started working with multiples of it. One of these multiple kind of stuck to the field: we are talking of the byte (symbol $\text{B}$), a group of 8 bits.

With 8 bits we can store exactly $256$ values, since $2^8 = 256$. Shall we list them? Just a bit!

\begin{align*} 00000000\\ 00000001\\ 00000010\\ 00000011\\ 00000100\\ ...\\ 11111100\\ 11111101\\ 11111110\\ 11111111 \end{align*}

With $256$ possible states, computers started storing letters (both uppercase and lowercase), numbers, symbols: each of these associated to a specific 8-bit string.

Fun fact: you can mechanically simulate bits with gears, where the smallest gear is the lowest bit. Check the animations in to visualize such a situation.

That's why the byte remained in common use. Let's check the multiples of the byte. As for the bit, we can have both decimal and binary multiples. For many reasons, the binary one are more common.

• The kibibyte: $1\ \text{KiB}=1024\ \text{B}$;
• The gibibyte: $1\ \text{GiB}=1024^2\ \text{B}$;
• The tibibyte: $1\ \text{TiB}=1024^3\ \text{B}$;

And so on. The decimal multiples are similar: the kilobyte ($\text{kB}$), the gigabyte ($\text{GB}$).

On most memories producers use the name of the decimal multiple, but the capacity in binary multiples. For example, when you buy an $1\ \text{TB}$ hard disk, you are actually buying an $1\ \text{TiB}$ hard disk. The difference, however is similar.

## The conversion of byte multiples

To calculate the bytes in a specific multiple, or to convert byte multiples from binary to decimal and the other way round, we use the same mechanics outlined before.

## How to use our byte converter

Our byte converter offers you many combinations of common — and less common — measurement units for data storage and transfer. Choose the units you are analyzing in our byte conversion tool, and input the value.

We chose some of the most common for you already!

Davide Borchia
B
kB
MB
GB
TB
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