Discovery · Lesson 02

How is digital information measured?

Bits describe information one binary choice at a time. Octets group those bits, while prefixes help us describe data sizes and network rates at a useful scale. For example, kB means 1,000 octets, while KiB means 1,024 octets because the i marks a binary prefix. The full binary names are kibibyte (KiB), mebibyte (MiB), gibibyte (GiB), and tebibyte (TiB).

Compare the scales

Decimal and binary prefixes use different powers.

The prefix tells you how many units are grouped together. Decimal prefixes use powers of 1,000, while binary prefixes use powers of 1,024. The letter i identifies a binary prefix.

How do we get from KiB to MiB?Start with 1 KiB = 1,024 octets. One MiB contains 1,024 KiB, so 1 MiB = 1,024 x 1,024 octets = 1,048,576 octets. The next step follows the same rule: 1 GiB = 1,024 x 1,024 x 1,024 octets = 1,073,741,824 octets.
103

kB / KiB

1 kB = 1,000 octets
1 KiB = 1,024 octets

106

MB / MiB

1 MB = 1,000,000 octets
1 MiB = 1,048,576 octets

109

GB / GiB

1 GB = 1,000,000,000 octets
1 GiB = 1,073,741,824 octets

1012

TB / TiB

1 TB = 1,000,000,000,000 octets
1 TiB = 1,099,511,627,776 octets

Example: 10 GB is smaller than 10 GiB.10 GB contains 10,000,000,000 octets, while 10 GiB contains 10,737,418,240 octets. Network rates and storage labels often use decimal units; operating systems and memory tools may use binary units.

Start with the smallest unit

A bit carries one binary value.

A bit is short for binary digit. It has only two possible values: 0 or 1. A bit can describe a logical state, a flag, or one decision in a binary representation. A physical system may carry that bit with voltage, light, radio energy, or another measurable signal.

A bit is useful because it gives digital systems a simple building block for representing, storing, processing, and transmitting information. Networks send long sequences of bits across links, and devices interpret those sequences according to shared rules.

An octet is a group of exactly eight bits. The word octet avoids ambiguity because a byte is not guaranteed to mean eight bits on every historical system, although modern computers almost universally use an eight-bit byte.

One octet contains eight bits.That gives 28 = 256 possible patterns, from 00000000 to 11111111. The pattern 01100001 is hexadecimal 0x61, and represents the lowercase letter a in ASCII and UTF-8.

Make large quantities readable

Prefixes scale bits and octets.

Writing millions or trillions of individual bits is inconvenient, so we use prefixes. Network rates normally use decimal prefixes: each step multiplies the quantity by 1,000. Storage and memory contexts may also use binary prefixes, where each step multiplies by 1,024.

103

kilo

1 kbit = 1,000 bits
1 kB = 1,000 bytes

106

mega

1 Mbit = 1,000,000 bits
1 MB = 1,000,000 bytes

109

giga

1 Gbit = 1,000,000,000 bits
1 GB = 1,000,000,000 bytes

1012

tera

1 Tbit = 1012 bits
1 TB = 1012 bytes

1015

peta

1 Pbit = 1015 bits
1 PB = 1015 bytes

1018

exa

1 Ebit = 1018 bits
1 EB = 1018 bytes

1021

zetta

1 Zbit = 1021 bits
1 ZB = 1021 bytes

1024

yotta

1 Ybit = 1024 bits
1 YB = 1024 bytes

1027

ronna

1 Rbit = 1027 bits
1 RB = 1027 bytes

1030

quetta

1 Qbit = 1030 bits
1 QB = 1030 bytes

Binary prefixes have different names.1 KiB = 1,024 bytes, 1 MiB = 1,024 KiB, 1 GiB = 1,024 MiB, 1 TiB = 1,024 GiB, and 1 PiB = 1,024 TiB. The i identifies a binary prefix.

Practice the relationship

Bits and octets convert by a factor of eight.

The capitalisation matters: lowercase b means bit, while uppercase B means byte or octet. To convert bits to octets, divide by eight. To convert octets to bits, multiply by eight.

DECIMAL CONVERSION100 bits = 12.5 octets1 octet = 8 bits. Decimal prefixes use powers of 1,000.

Do not confuse quantity and speed

A file size is not a network rate.

Data size tells how much information exists, such as 700 MB. A data rate tells how quickly a link transfers information, such as 100 Mbit/s. Time connects them: transfer time is approximately data size divided by the useful rate, after converting both to the same unit.

FILE700 MBquantity of data
LINK100 Mbit/srate of transfer
RESULTabout 56 s700 MB = 5,600 Mbit
100 Mbit/s is not 100 MB/s.Divide the advertised bit rate by eight: 100 Mbit/s ÷ 8 = 12.5 MB/s. Real application speed is usually lower because of protocol overhead, contention, signal conditions, and other limits.

Knowledge check

Test your unit model

Answer ten questions. The answer order changes each time.

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