Discover How Computers Speak in Binary

Ever wondered how your computer speaks its own language? This article guides you through the basics of bits and bytes, uncovering the mechanisms computers use to store and convey data. We'll see how combinations of bits can represent anything from a single number to a video file and I'll even show you how to understand your internet speed!

Bits and Bytes

The Smallest Bit

A 'bit' is the smallest unit of data that a computer can store. It represents a binary state. The easiest way to understand this is that a bit can be either a 1 or a 0.

But a single bit on its own can only represent two data points: 1 or 0. In order for a computer to make use of data, it needs more capacity. The more bits we combine together, the more unique values we can use and therefore the greater our capacity to represent data. The mathematical rule is n-bits has 2ⁿ unique values:

1-bit makes 2 unique values: 0 & 1

2-bit makes 4 unique values: 00, 01, 10, 11

4-bit makes 16 unique values ranging from 0000 to 1111

6-bit makes 64 unique values ranging from 000000 to 111111

8-bit makes 256 unique values ranging from 00000000 to 11111111

Bytes of Information

In computing, we call an 8-bit pattern a 'byte'. As shown above, this means a single byte can store any number between 0 and 255 (256 unique values). If we need to store numbers higher than 255 then we can use multiple bytes. And as we start to use multiple bytes to represent a single data point, the range of numbers we can represent becomes staggering. As an example a 4-byte number (32 bits) has 4,294,967,296 unique values (2³²)!

"But not all data we store is numbers", I hear you cry! "Some of us want to store text and emojis and stuff"

That is a great point. Thanks for speaking up.

To solve this problem we create agreements. For example, when a computer is storing text it follows a standard that says the binary number 1100001 represents the letter a, the binary number 1100010 represents the letter b and so forth. Once such agreement is ASCII. Different types of data (audio, video etc) have their own agreements so that a computer can understand what the binary being stored represents.

Measuring Data Storage

A single byte is an extremely small unit of storage. You could use it to store a small number or a single character. So it quickly becomes necessary to use a naming standard for large numbers of bytes.

You've likely heard of the term 'kilobyte' before. The prefix 'kilo' is traditionally used to represent 10³ (10 x 10 x 10 or 1000) as in 'kilometre' and 'kilogram'. For computers, this means a kilobyte should be 1000 bytes…actually it is roughly 1000 bytes.

What do you mean 'roughly'?

This bit can get confusing (pun intended ) and does involve a some maths. Because computers are binary beasts, they work best with numbers that are a power of 2. As a result we bend the naming rules a bit. The nearest number to a thousand that is also a power of 2 is 2¹⁰ which is 1,024. Which is why 1 kilobyte = 1,024 bytes.

Names for Storage

kilobyte = a thousand = KB = 2¹⁰ = 1,024 bytes

megabyte = a million = MB = 2²⁰ = 1,024 KB

gigabyte = a billion = GB = 2³⁰ = 1,024 MB

terabyte = a trillion = TB = 2⁴⁰ = 1,024 GB

petabyte = a quadrillion = PB = 2⁵⁰ = 1,024 TB

Measuring Data Transmission

Data transmission is the transfer of data from one device to another. That could be from your computer to an external hard drive. It also includes browsing the internet and watching YouTube, as your device has to download the content before you can consume it. Have you ever renewed your internet contract and wondered what the advertised speeds actually meant? This is where we shine a light on that.

Measuring the speed of data transmission differs from measuring data storage. Data is transferred one bit at a time, albeit at an extremely fast rate! This makes measurement simple because we track the number of bits per second (bps) transferred.

We can use the same prefixes as we do for measuring data storage (kilo, Mega, Giga, etc), with the key difference being that we can go back to using powers of 10.

Names for Transmission Speeds

kilobits per second = a thousand = kbps = 10³ = 1,000 bps

megabits per second = a million = Mbps = 10⁶ = 1,000 kbps

gigabits per second = a billion = Gbps = 10⁹ = 1,000 Mbps

terabits per second = a trillion = Tbps = 10¹² = 1,000 Gbps

What's up with the little k in kbps?

Note the rather confusing inconsistency with capitalisation: the lowercase 'k' represents 1,000 in decimal measurements (used to measure data transmission), unlike data storage which often uses a capital 'K' to denote binary measurement We are not so consistent with mega, giga etc.

This post is part of a series: Computer Science Intro

1. Binary Made Easy
2. How Computers Speak in Binary

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