Bits, Bytes and Prefixes once and for All!

Working with bits and bytes and everything in between can be confusing if you aren’t familiar with how it all works. If you wanted to know why your hard drive is actually a lot smaller than what is written on the box and that’s considered fair game, read on. If you just want a go-to guide to send to your friends, then this guide is also for you. Hopefully this can clear up all the incorrect usage of terms on the internet once and for all! And yeah, I know I’m dreaming…

Binary Matrix Style

Bits

Definition: 1 bit is the smallest divisible amount of digital data. One bit will be either represented by a 0 or 1 in binary: on or off.

Abbreviation: b

Bytes

Definition: 8 bits of data form one byte. Bytes are the most commonly referred to unit in digital storage.

Abbreviation: B

SI Prefixes

Definition: The SI (from the French Standard International) units are prefixes which multiply the value of bits or bytes. It is a base 10 system.

Abbreviations:

PrefixSymbol10n
 English Name
Number
 Kilo k103 Thousand1,000
 Mega M106 Million1,000,000
 Giga G109 Billion1,000,000,000
 Tera T1012 Trillion1,000,000,000,000
 Peta P1015 Quadrillion1,000,000,000,000,000
 Exa E1018 Quintillion1,000,000,000,000,000,000

Base 2 Prefixes

Definition: These prefixes are used almost exclusively in computer science to account for the fact that computers inherently work on a base 2 system rather than a base 10 system.

Abbreviations:

 PrefixSymbol
 2n
 Number
 Kibi Ki 210  1024
 Mebi Mi 220 1,048,576
 Gibi Gi 230 1,073,741,824
 Tebi Ti 240 1,099,511,627,776
 Pebi Pi 250 1,125,899,906,842,624
 Exbi Exi 260 1,152,921,504,606,846,976

Working with Units

It is relatively simple to combine the prefixes with bits or bytes if you remember the scales. Let’s consider a few examples:

1KB = 1 kilobyte
1Kb = 1 kilobit
1Mb = 1 megabit
1KiB = 1 Kibibyte
1Tib = 1 Tebibit

When working with the commonly used SI prefixes, each “step up” is 1000 times larger than the previous one:

1000B = 1KB
1000KB = 1MB
1000MB = 1GB…

It is common to use bits when referring to networking applications, while most other uses will normally be presented in bytes. For example:

Network adapters are commonly 100 Mb/s (100 megabits per second)
Hard drive capacities now reach up to 2 TB (2 terabytes)

Converting from bits to bytes is equally simple; all you need to know is how to divide by 8:

Uncapped, ADSL can reach up to 8 Mb/s (8 megabits per second)
This is equivalent to 1 MB/s (1 megabyte per second as there are 8 bits per byte)

Another case where proper usage of terms can be confusing is with HDD capacities; the reason that your 1 terabyte hard drive does not format to a full 1000 gigabytes is because they are rated using the SI base 10 system, while computers actually work on a base 2 system. For example, see the conversion done in Wolfram|Alpha.

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