Data handled by computers is represented by combinations of 0s and 1s. The basic unit of this representation is the bit, and a unit made up of eight bits is the byte.

The number of bits relates to the number of combinations that can be represented, while the number of bytes relates to the size of data. This article organizes the relationship between the two from two perspectives: combinations and units.

1.1.1 What Is a Bit?

A bit is a single binary digit that takes a value of 0 or 1. One bit can distinguish between two possibilities: 0 and 1.

In computers, information can be handled by associating the states of an electrical signal with 0 and 1. Here, 0 and 1 are representations used to distinguish between two different states.

Arranging multiple bits makes it possible to represent more combinations than a single bit can. For example, two bits give four combinations: 00, 01, 10, and 11. Because 01 and 10 differ in order, they are separate combinations.

1.1.2 Number of Bits and Number of Combinations

Because each digit takes either 0 or 1, adding one bit doubles the number of combinations. Therefore, the number of combinations $N$ that can be represented with $n$ bits is given by the following equation.

Here, $n$ is the number of bits and $N$ is the number of combinations.

Table 1.1-1 Number of Bits and Number of Combinations That Can Be Represented

Number of bits	Calculation	Number of combinations
1 bit	$2^1$	2
2 bits	$2^2$	4
3 bits	$2^3$	8
4 bits	$2^4$	16
8 bits	$2^8$	256
16 bits	$2^{16}$	65,536

For example, consider assigning a different bit string of the same length to each of six kinds of objects. Two bits are not enough because they give only four combinations. Three bits give eight combinations, so a separate bit string can be assigned to each of the six kinds.

In this way, the number of bits required is determined by comparing the number of kinds of objects to be distinguished with the number of combinations available.

1.1.3 What Is a Byte?

A byte is a unit that groups eight bits together. The uppercase B is used as its unit symbol, and the bit is written as bit.

For example, 16 bits are 2 bytes, and 32 bits are 4 bytes. To convert bytes to bits, multiply by 8; to convert bits to bytes, divide by 8.

The number of combinations that one byte can represent is 256, the same as for 8 bits. “8 bits,” which expresses the length of data, and “256 combinations,” which expresses the number of combinations, are different quantities.

For example, 2 bytes are 16 bits, so the number of combinations is 65,536. Although the length is twice that of 1 byte, the number of combinations is not twice 256.

1.1.4 The Difference Between “256 Combinations” and “0 to 255”

When the 256 bit strings of one byte are mapped one to one onto the integers from 0 to 255, the values that can be represented range from 0 to 255.

Because 0 is also counted as a value, there are 256 values from 0 to 255. The number of values that can be represented is 256, and the maximum value is 255; it is important not to confuse the two.

The fact that “one byte can distinguish 256 combinations” and the question of “which integer a bit string is read as” need to be considered separately.

1.1.5 Units for Large Amounts of Data

To express large amounts of data, a prefix is attached to the byte. Here, prefixes based on powers of 10 are distinguished from prefixes based on powers of 2.

Table 1.1-2 Byte Units Based on Powers of 10 and Powers of 2

Unit	Name	Number of bytes
kB	kilobyte	1,000 B
MB	megabyte	1,000,000 B
GB	gigabyte	1,000,000,000 B
KiB	kibibyte	1,024 B
MiB	mebibyte	1,048,576 B
GiB	gibibyte	1,073,741,824 B

For example, 1 MB is 1,000,000 B and 1 MiB is 1,048,576 B, so they are not the same size. Prefixes that represent powers of 2 contain an i, as in Ki, Mi, and Gi.

When reading an amount of data, check not only the number but also whether the unit is bit or B and whether the prefix is M or Mi.

Summary

A bit is a single digit that takes a value of 0 or 1, and $n$ bits can represent $2^n$ combinations. Because one byte is 8 bits, one byte has 256 combinations.

The length of data, the number of combinations, and the value obtained when a bit string is read as an integer should each be considered separately. For large amounts of data, also pay attention to differences in units caused by prefixes, such as MB and MiB.

About This Article

Sources

• Ministry of Education, Culture, Sports, Science and Technology (MEXT), “D Information Technology Training (D1),” Case 1-2 (in Japanese)
• National Institute of Standards and Technology (NIST), “CSRC Glossary: bit”
• National Institute of Standards and Technology (NIST), “CSRC Glossary: Byte”
• National Institute of Standards and Technology (NIST), “Prefixes for binary multiples”

(Last accessed: October 20, 2026)


*This article was compiled based on the author’s understanding and practical knowledge, with reference to the above literature.