随笔

digit bit and bytes

2026-09-24

shuiming.....bit digit bytes in details.

deepseek.....Let’s break down bits, digits, and bytes in detail, including how they relate to the memory units shown in commands like free -h.

1. Bit (Binary Digit)

  • Definition: A bit is the smallest unit of data in computing.
  • It is short for binary digit and can have only two possible values: 0 or 1.
  • All digital data (text, images, programs, memory contents) is ultimately stored and processed as a series of bits.

Example The number 1011 is four bits. It represents the decimal number 11 (1×8 + 0×4 + 1×2 + 1×1).

2. Digit

In everyday language, a digit is a single symbol used to represent numbers (0–9 in decimal). In computing, we primarily use:

  • Binary digit (bit) – base‑2, symbols 0 and 1.
  • Hexadecimal digit – base‑16, symbols 0–9 and A–F (often used to represent groups of 4 bits compactly).
  • Decimal digit – base‑10, symbols 0–9 (used when we talk about “kilobytes” = 1000 bytes, for example).

So when you hear “digit” in computing, it usually refers to a bit (binary digit) unless otherwise specified.

3. Byte

  • Definition: A byte is a unit of digital information that consists of 8 bits (in modern systems – historically, the size of a byte could vary, but 8 bits is now the universal standard).
  • Why 8 bits?
  • Early computers used 6‑bit or 7‑bit codes (e.g., ASCII was originally 7 bits).
  • 8 bits became popular because it can represent 256 different values (2⁸ = 256), which is enough to encode all English letters, digits, punctuation, and many control characters.
  • It also aligns nicely with powers of two, which is fundamental in binary hardware.
  • Smallest addressable unit: In most computer architectures, each byte has its own unique memory address. You cannot directly address a single bit – you must read/write entire bytes (or multiples of bytes) at once.
  • Abbreviation: Usually denoted by uppercase B (as in KB, MB, GB, where B = byte). Be careful: lowercase b normally means bit.

Examples of byte usage - One ASCII character (like A) typically occupies 1 byte (8 bits). - An image file of 5 MB is approximately 5 million bytes.

4. Units for Large Amounts: Decimal vs Binary Prefixes

When dealing with memory, storage, or file sizes, we use prefixes like kilo, mega, giga, tera, etc. But there are two different systems in use:

Prefix Decimal (SI) Binary (IEC) Factor (Decimal) Factor (Binary)
Kilo KB KiB 10³ = 1,000 2¹⁰ = 1,024
Mega MB MiB 10⁶ = 1,000,000 2²⁰ = 1,048,576
Giga GB GiB 10⁹ = 1,000,000,000 2³⁰ = 1,073,741,824
Tera TB TiB 10¹² = 1,000,000,000,000 2⁴⁰ = 1,099,511,627,776
  • Decimal (SI) prefixes (KB, MB, GB) are based on powers of 10, used mainly by hard drive manufacturers and some software (like Windows incorrectly).
  • Binary (IEC) prefixes (KiB, MiB, GiB) are based on powers of 2, used by most operating systems and technical tools to accurately describe memory sizes because computers work in binary.

Important - 1 KiB = 1024 bytes - 1 KB = 1000 bytes

The difference becomes significant at larger sizes: 1 GiB ≈ 1.074 GB (about 7.4% larger).

5. What free -h Uses

The command free -h (or free --human) displays memory sizes using binary prefixes (KiB, MiB, GiB) by default. That’s why you saw 5.7Gi, 2.2Gi, etc. If you want decimal (SI) units, you can use free -h --si, which will show 5.7G (meaning 5.7 gigabytes = 5.7 × 10⁹ bytes) instead.

From your earlier output:

Mem:           5.7Gi       2.2Gi       1.3Gi       3.5Mi       2.3Gi       3.5Gi
  • 5.7Gi = 5.7 × 2³⁰ bytes = 6,118,115,328 bytes (approximately 6.12 GB decimal).
  • 3.5Mi = 3.5 × 2²⁰ bytes = 3,670,016 bytes.

So the memory values are shown in gibibytes and mebibytes, not gigabytes/megabytes.

6. Why This Matters

  • Memory capacities (RAM, cache) are typically expressed in GiB or MiB because RAM is addressed in binary multiples (address lines correspond to powers of two).
  • Storage devices (HDD, SSD) are often marketed using GB (decimal), which makes a 1 TB drive appear larger than it actually is when measured in TiB (a 1 TB drive is about 0.909 TiB).
  • Network speeds are commonly measured in bits per second (Mbps, Gbps), not bytes. To convert: 8 bits = 1 byte, so a 100 Mbps connection transfers at most 12.5 MB per second (before overhead).

Summary Table

Term Meaning Size / Value
Bit Single binary digit (0 or 1) Smallest unit
Byte 8 bits 1 B = 8 b
Kilobyte (KB) 1000 bytes (decimal) 10³ bytes
Kibibyte (KiB) 1024 bytes (binary) 2¹⁰ bytes
Megabyte (MB) 1,000,000 bytes 10⁶ bytes
Mebibyte (MiB) 1,048,576 bytes 2²⁰ bytes
Gigabyte (GB) 1,000,000,000 bytes 10⁹ bytes
Gibibyte (GiB) 1,073,741,824 bytes 2³⁰ bytes

Final Word

  • A bit is a single binary digit.
  • A byte is 8 bits and is the standard unit of memory/storage.
  • When you see GiB, MiB, KiB, it’s the binary (power‑of‑2) measurement – which is what free -h shows.
  • The term “digit” in computing usually refers to a binary digit (bit), but can also mean a decimal digit in other contexts.