Units
Units
We’ll be using various units. Just in case you’re not familiar with units we may use, here’s a handy reference.
International System of Units (SI)
You’ll often see whatever units we may encounter in this course prefixed with standard SI prefixes. Prefixes are used to indicate multiples or submultiples (divisions) of the original unit.
Big stuff / lots of stuff
| prefix | symbol | base 10 | decimal | colloquially |
|---|---|---|---|---|
| peta | P | 10^{15} | 1,000,000,000,000,000 | quadrillion |
| tera | T | 10^{12} | 1,000,000,000,000 | trillion |
| giga | G | 10^{9} | 1,000,000,000 | billion |
| mega | M | 10^{6} | 1,000,000 | million |
| kilo | k | 10^{3} | 1,000 | thousand |
Small stuff / not much stuff
| prefix | symbol | base 10 | decimal | colloquially |
|---|---|---|---|---|
| centi | c | 10^{-2} | 0.01 | hundredth |
| milli | m | 10^{-3} | 0.001 | thousandth |
| micro | \mu | 10^{-6} | 0.000001 | millionth |
| nano | m | 10^{-9} | 0.000000001 | billionth |
If we say some supercomputer can perform 2.5 petaflops per second, that means it can perform 2.5 \times 10^{15} flops per second, or 2,500,000,000,000,000 flops per second. (Don’t worry about what a “flop” is right now. We’ll get to that in due course.)
If we say an integrated circuit is on a scale of eight nanometers, that means that each transistor is approximately eight nanometers in size. That’s eight billionths of a meter or 8 \times 10^{-9} or 0.000000008 meters. (That’s about three ten-millionths of an inch for us Yanks, but we’ll be sticking with SI units.)
Frequencies
Frequency refers to the number of occurrences of some kind of event over time. For example, the frequency of sunrises is once per day. Your dentist says your tooth-brushing frequency should be three per day.
Your computer has a clock and clocks run at certain frequencies. Computer clock speed, also known as clock rate or CPU frequency, refers to the rate at which a processor executes its instructions. Nowadays, this is usually measured in gigahertz (GHz). Essentially, it dictates how many calculations a CPU can perform per second.
What’s a hertz? The hertz (Hz) is the SI unit of frequency, measuring the number of occurrences of a repeating event per second.
So, if some processor runs at 4.5 GHz, and some instruction takes one clock cycle, then that processor can perform that operation 4,500,000,000 times per second.
Bit
A bit—short for binary digit—is a unit of information. A bit can have a value of zero or one. That’s it. Everything that goes on in your computer involves bits of information—strings of zeros and ones. This includes data and instructions.
Here’s a bit.
0
Here’s another bit.
1
See? Not much to them.
When we abbreviate units, “bits” is abbreviated with a lower-case “b”. Hence, 20 kb is 20 kilobits or 20,000 bits.
Bytes and nibbles
While bits are fundamental, they are rather tiny amounts of information. Most digital information is represented, transmitted, manipulated, and stored in slightly larger chunks: bytes.
Bytes, at least for our purposes, consist of eight bits. Why eight? Well, it’s a power of two (2^3) and it’s about the size we need to represent symbols in a small alphabet.
Here’s the number 21 represented in binary as a byte of eight bits.
00010101
There are deviations from the so-called 8-bit byte, but they’re mostly special cases or historical curiosities, so we’ll mention this and then promptly forget about it.
Sometimes we may refer to a byte as consisting of two 4-bit nibbles (bytes, nibbles, get it?). For ease of reading, we might write the number 21 in binary, thus:
0001 0101
When we abbreviate units, “bytes” is abbreviated with a upper-case “B”. Hence, 1 MB is one million bytes.
Word
A word is a fixed-size block of bytes, the size of which depends on the CPU. Words are typically 16, 32, or 64 bits—that’s two, four, or eight bytes.
The computer on which I type this has an architecture with a 64-bit word size, or eight bytes.
Base 10 (decimal) vs base 2 (binary)
The SI units above are all with respect to our base 10 (decimal) counting system. However, in computers most everything is binary, and things come in groups of two or powers of two.
Accordingly, when we talk about large numbers of bits or bytes, we may use different prefixes than are used in SI units. This can cause some confusion, so be sure you understand the difference.
Let’s say some specification says that such and such machine or storage device has 1 MB of RAM (memory). Does this mean that it has one million bytes of memory? No. It does not. Everything comes in twos or powers of twos, so 1 MB usually means 1,048,576 bytes (that’s 2^{20} bytes—a power of two). So the 1 MB is really an approximate value.
Here are the alternative prefixes you may see when dealing with multiple-byte units. These are all based on powers of 1024, which itself is a power of two (1024 = 2^{10}).
| prefix | symbol | base 2 | power of 1024 | decimal |
|---|---|---|---|---|
| kibi | Ki | 2^{10} | 1 | 1,024 |
| mebi | Mi | 2^{20} | 2 | 1,048,576 |
| gibi | Gi | 2^{30} | 3 | 1,073,741,824 |
| tebi | Ti | 2^{40} | 4 | 1,099,511,627,776 |
Frankly, these sound a little silly when spoken, and unless you’re a hardware engineer (or in a course on computer organization or architecture) you’re unlikely to hear them used often. You will see them when looking at specifications of computers and storage devices.
Examples of scale
Physical measurement
| unit | example |
|---|---|
| nm (nanometer) | a decent sized molecule (that’s pretty small) |
| \mum (micron) | width of spider silk is about 5 microns |
| mm (millimeter) | thickness of your thumbnail |
| m (meter) | my youngest son is about 1.85 meters tall (6’1”) |
Bits and bytes
| unit | example (approximate for larger units) |
|---|---|
| bit | 0 or 1; true or false |
| byte | encoding of the letter “A” |
| kilobyte or kibibyte | the text of a poem |
| megabyte or mebibyte | the text of a novel; a minute or two of MP3 audio; a modest resolution digital photo |
| gigabyte or gibibyte | 200 MP3 audio songs; 1,000 novels |
| terabyte or tebibyte | 100 movies; 5 million pages of documents |
Check-in
On my computer the word size is 64-bit. How many bytes is that? How many nibbles?
If we were to type a 64-bit word right here, would it be longer than this line?
There are approximately 100 kilohairs on a human head. How many hairs is that? How many megahairs is that?
Let’s say a typical human thumbnail is about 400 mm2. How many transistors can fit in such an area if each transistor is 10 nm on a side? (You may assume that both the thumbnail-sized area and a transistor are square.)
Consumer internet upload rates in the USA vary by service provider, but 20 Mb / s is typical. How many novels can a typical user upload in an hour assuming an uninterrupted connection?
Typical upload rates in Chile are about 180 Mb / s. How long would it take someone in Chile to upload the same number of novels?
The 5.25-inch floppy disks used in the 1981 IBM PC 5150 could store 360 kB of information. Adobe Acrobat Reader is about 1.86 GB in size. How many floppy disks would it take to store Adobe Acrobat Reader?
CD quality audio is 16 bits per sample, with 44.1 kHz sampling rate, and two (stereo) channels. About how big would a one minute uncompressed audio file be, given CD quality?
Bluetooth has a typical data rate of about 1 Mb / s. Why can’t we stream CD quality audio over Bluetooth?
How many times faster would Bluetooth need to be able to stream CD quality audio?
Copyright © 2025 Clayton Cafiero
No generative AI was used in producing this material. This was written the old-fashioned way.