A bit (b) is the basic unit of almost every modern computer system. The word bit is a contraction of the term binary digit.

A bit is the building block for the numbers, languages, and almost every aspect of computer operation. It is also the smallest (irreducible) unit of information in those computers.

A binary unit can only have two values or logical states, typically the values are 0 and 1. But the values could also be 'Off' and 'On', 'False' and 'True' or 'No' and 'Yes'.

You will notice that I have reversed the common convention of listing the positive value first. Normally, we would say 'On' and 'Off', 'True' and 'False', etc. The reason I have done this is to emphasize that the initial, default or unassigned state of a bit is normally zero or not set.

 

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That is enough information to understand what a bit is. Read on if you want more understanding of binary systems, binary numbering and bit-length.

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There are many binary systems in the world arounds us

The following table illustrates some other examples of binary systems.

Table 1 — Binary systems have two discrete states
	State 1	State 2
Logic	False	True
Decision making	No	Yes
Electrical switch	Off	On
Electrical charge	- Negative	+ Positive
Probability	0%	100%
Morse code	· Dot	– Dash
Door	Closed	Open
Lever	Down	Up
Level	Low	High

 

Binary systems are used to store information

In 1725, a textile loom was partially automated by using patterns recorded by punching holes in a paper roll. The loom was programmed by using the pattern to guide the machine. The nineteenth-century piano roll operates on the same principle.

Two principles underly this method of storing and processing information:

1. The pattern is stored even when the machine is not processing the pattern.
2. When the machine is operating, nothing happens or changes unless there is a transition from no hole to a hole or from a hole to no hole. That is almost exactly what happens in modern computer processing. We just use electrical signals and newer types of media.

Those early paper rolls are part of the development of storage media that ultimately led to the media we use today.

Table 2 — Binary storage media
	State 1	State 2
Paper tape (since 1725 but now obsolete)	No hole	Hole
Cards (since 1728 but now obsolete)	No hole	Hole
Magnetic tape (since 1951 but tending to become obsolete)	Not magnetized	Magnetized
Magnetic memory (since 1951 but new developments)	Not magnetized	Magnetized
Magnetic disk (since 1956)	Not magnetized	Magnetized
Magnetic stripe card (since 1960 but increasingly chip-based)	Not magnetized	Magnetized
Optical disk (since 1970, e.g. CD, DVD, BD)	No pit	Pit

 

Binary counting is used to create more than two values

With one bit we can have two values. To get more than two values we can combine bits to create larger values.

The value of a computer bit is a binary or Base-2 number, 0 or 1. The numbers we normally use are the decimal or Base-10 digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) so counting looks very different in binary as shown in the following table. As we join bits together we can make larger binary numbers.

Our decimal system has a decimal progression where the order of magnitude is 10: 1, 10, 100, 1,000, 10,000, 100,000, 1,000,000, etc. The equivalent binary progression where we join bits together is also 10, 100, 1000, 10000, 100000, 1000000, etc. but the order of magnitude is only 2 so the decimal equivalents are a lot less: 2, 4, 8, 16, 32, 64, 128, 256, 512, 1,024 etc.

Table 3 — Counting in binary
Number of bits	Binary Base-2	Decimal Base-10	Hexadecimal Base-16
1	0	0	0
	1	1	1
2	10	2	2
	11	3	3
3	100	4	4
	101	5	5
	110	6	6
	111	7	7
4	1000	8	8
	1001	9	9
	1010	10	A
	1011	11	B
	1100	12	C
	1101	13	D
	1110	14	E
	1111	15	F
5	10000	16	10

At this point, I've introduced hexadecimal (Base-16, 4-bit) values because you are likely to see these numbers in many places. Large binary numbers are unweildy and very hard to remember so hexadecimal has been a useful way to remember them. For example, decimal 42 is not too hard to remember as binary 101010 or hexadecimal 2A. But decimal 1,000,000 is very hard to remember as binary 11,110,100,001,001,000,000 but much easier as hexadecimal F4240.

We can indicate the Base for any number by appending it as a subscripted number. For example, binary 10000₂ = decimal 16₁₀ = hexadecimal 10₁₆. This is equivalent to the last row of Table 3 above.

 

Try binary counting for yourself

Try binary counting using your fingers. With ten fingers you can store 2¹⁰ = 1,024 values.

• 0 = finger down
• 1 = finger up

Why can I count much higher than using my fingers for decimal counting? When counting in decimal the number zero only needs to be represented by one finger but instead we use all ten so nine add no additional information. Binary counting is the most efficient method to use two finger positions because both finger positions always indicate unique values.

If you use three finger positions then ternary or trinary counting will work better. Binary counting can still be used but it will only be easy if the number of finger positions is a multiple of two. So four positions would give 1,048,576 values. That is 1,024 multiplies by 1,024 .

 

Try binary numbering using Windows Calculator

You can also try the various numbering systems for yourself using Windows Calculator.

From the Start Menu, select 'All programs', select 'Accessories', select 'Calculator'.

When the Calculator window appears, on the main menu select 'View'. On the drop-down menu select 'Programmer' for Windows Vista to 7 or select 'Scientific' for Windows XP.

Here you can enter digits in Decimal, Hexadecimal, Binary, and even Octal which is Base-8. For example, with the Dec button selected, type in the number 42 then select the button for the number system you want to view. Calculator displays the equivalent value for the number system you select.

 

Bit numbers you are likely to see on computer systems

Now let's have a look at some of the numbers you are likely to see on computer systems when you join bits together. If I have eight bits joined together then I can create an 8-bit value, with sixteen bits I can create a 16-bit value, and so on.

There are two values that you are likely to meet for each bit-length:

• The number of values that can be represented by that bit-length as shown in Table 4
• The actual values that can be stored by that bit-length as shown in Table 5.

The largest number that can be stored will be one less than the number of values because, as I said earlier, the default state for a bit is 0 so the first value will be zero. Using memory locations as an example, if I have 65,536 memory locations then the memory addresses will normally be from 0 to 65,535. The upper limit being one less than the number of memory locations.

Note that binary and hexadecimal representations don't use commas to separate every third order of magnitude as decimal does. Instead they tend to separate every fourth order (as four is a multiple of two) with a space or colon.

Table 4 — The number of values for a given bit-length
Number of bits	Decimal Base-10	Hexadecimal Base-16
8	256	100
16	65,536	1 0000
32	4,294,967,296	1 0000 0000
64	18,446,744,073,709,551,616	1 0000 0000 0000 0000

Now let's have a look at some of the numbers you are likely to see on computer systems when you join bits together. If I have eight bits joined together then I can create an 8-bit value, with sixteen bits I can create a 16-bit value, and so on.

Table 5 — The range of values for a given bit-length
Number of bits	Decimal Base-10	Hexadecimal Base-16
8	0 to 255	0 to FF
16	0 to 65,535	0 to FFFF
32	0 to 4,294,967,295	0 to FFFF FFFF
64	0 to 18,446,744,073,709,551,615	0 to FFFF FFFF FFFF FFFF

 

More binary numbers that you are likely to see

These numbers are smaller and are more likely to be seen in the detail of computing. They can be seen when editing disk data, viewing memory ranges, and working in the Windows registry.

Table 6 — The number of values available for a given bit-length
Number of bits	Binary Base-2	Decimal Base-10	Hexadecimal Base-16
1	1	1	1
	10	2	2
2	100	4	4
3	1000	8	8
4	1 0000	16	10
5	10 0000	32	20
6	100 0000	64	40
7	1000 0000	128	80
8	1 0000 0000	256	100
9	10 0000 0000	512	200
10	100 0000 0000	1,024	400
11	1000 0000 0000	2,048	800
12	1 0000 0000 0000	4,096	1000
13	10 0000 0000 0000	8,192	2000
14	100 0000 0000 0000	16,384	4000
15	1000 0000 0000 0000	32,768	8000
16	1 0000 0000 0000 0000	65,536	1 0000

 

As I said above, the lowest value is usually zero so the largest number will be one less than the number of values. These numbers look a lot different than in Table 6.

Table 7 — Maximum value for a given bit-length
Number of bits	Binary Base-2	Decimal Base-10	Hexadecimal Base-16
1	0	0	0
	1	1	1
2	11	3	3
3	111	7	7
4	1111	15	F
5	1 1111	31	1F
6	11 1111	63	3F
7	111 1111	127	7F
8	1111 1111	255	FF
9	1 1111 1111	511	1FF
10	11 1111 1111	1,023	3FF
11	111 1111 1111	2,047	7FF
12	1111 1111 1111	4,095	FFF
13	1 1111 1111 1111	8,191	1FFF
14	11 1111 1111 1111	16,383	3FFF
15	111 1111 1111 1111	32,767	7FFF
16	1111 1111 1111 1111	65,535	FFFF

 

Related Links

What is a byte? What is 8-bit? What is 16-bit? What is 32-bit? What is 64-bit? What is 128-bit? What is 256-bit?