Programming Languages - Bits and Bytes

Last Updated: 2024-01-21

1 byte = 8-bit integer, in the range 0 to 255

Bit vs Byte

bit: a single 0 or 1. 2 different values. The most basic unit of computing
byte: 1 byte = 8 bits = 2 hex = 256 different values. A.k.a "octet". Still "naked" 0s and 1s, can be interpreted in different ways.
characters:
- historically, 1 byte (8 bits) is used to encode a single character: ASCII uses 7 bits, 128 code points, more than enough for English characters (both lowercase and uppercase). One extra bit can be used as a parity bit.
- now one character may need more than one byte to store, depend on the encoding.

Multiple-byte Units

Unit	Abbrev.	Bytes	Unit	Abbrev.	Bytes
kB	kilobyte	1000	KiB	kibibyte	1024
MB	megabyte	10002	MiB	mebibyte	10242
GB	gigabyte	10003	GiB	gibibyte	10243
TB	terabyte	10004	TiB	tebibyte	10244
PB	petabyte	10005	PiB	pebibyte	10245
EB	exabyte	10006	EiB	exbibyte	10246
ZB	zettabyte	10007	ZiB	zebibyte	10247
YB	yottabyte	10008	YiB	yobibyte	10248

Note if there's an i in the unit name: with an i, it is binary, otherwise decimal.

For example:

terabyte (TB): 1012, or 10004, or 1,000,000,000,000 bytes
tebibyte (TiB)： 240, or 10244, or 1,099,511,627,776 bytes, roughly 1TiB = 1.1TB

Real world examples

3.5 inch Floppy Disk: 1,440 KiB = 1.47 MB = 1.41 MiB
CD: up to 700 MB
DVD: 4.7 GB = 4.38 GiB for a single-layered, single-sided disc
Blu-ray: 25 GB for single-layer
The Complete Works of William Shakespeare would occupy about 5,600,000 bytes when written in plain text without formatting.

Bit Manipulation

AND(`&`)

| AND | 0   | 1   |
| --- | --- | --- |
| 0   | 0   | 0   |
| 1   | 0   | 1   |

OR(`|`)

| OR  | 0   | 1   |
| --- | --- | --- |
| 0   | 0   | 0   |
| 1   | 0   | 1   |

XOR(`^`)

| XOR | 0   | 1   |
| --- | --- | --- |
| 0   | 0   | 0   |
| 1   | 0   | 1   |

NOT(`!`)

| NOT |     |
| --- | --- |
| 0   | 1   |
| 1   | 0   |

Basic Operations

Bitwise And: &
Bitwise exclusive OR: ^
Bitwise inclusive OR: |
Unary bitwise complement: ~
Signed left shift: <<
Signed right shift: >>
Unsigned right shift: >>>

By Language

Java

int bitmask = 0x000F;
int val = 0x2222;

System.out.println(val & bitmask);
// 2

System.out.println(~256);
// -257

Python

bytes is an immutable array of bytes (PyString)
bytearray is a mutable array of bytes (PyBytes)
memoryview is a bytes view on another object (PyMemory)

bytes literal: b'...'

str objects: hold character data
bytes objects: hold raw bytes

Indexing returns a integer:

>>> a = b'asdf'
>>> a
b'asdf'
>>> a[0]
97

while str returns a character:

>>> b = 'asdf'
>>> b
'asdf'
>>> b[0]
'a'

Assigning or comparing an object that is not an integer to an element causes a TypeError exception.
Assigning an element to a value outside the range 0 to 255 causes a ValueError exception.

string must comes with encoding

bytearray:

>>> a = bytearray("123", 'utf-8')
>>> a[0]
49
>>> a[1]
50

bytes:

>>> a = bytes('abc', 'utf-8')
>>> a
b'abc'

Endianness

Endianness: the order of the bytes

Big vs Little

big-endian: the most significant byte first
little-endian: the least significant byte first

Other names:

Network byte order: big-endian

Example:

0A 0B 0C 0D

Big-endian: stored as 0A 0B 0C 0D in memory
Little-endian: stored as 0D 0C 0B 0A in memory

Why Little-endian

A 32-bit memory location with content 4A 00 00 00 can be read at the same address as either 8-bit (value = 4A), 16-bit (004A), 24-bit (00004A), or 32-bit (0000004A), all of which retain the same numeric value.

Systems

big endian: Java, IPv6 (network byte order), IBM z/Architecture mainframes,
little endian: Intel x86 processor

In Action

In Python:

>>> import struct
>>> struct.pack("<I", 1)
b'\x01\x00\x00\x00'
>>> struct.pack(">I", 1)
b'\x00\x00\x00\x01'

where < means little-endian, and > means big-endian. I for 32-bit unsigned integer, so it takes 4 bytes. In little-endian, byte \x01 is stored first, while in big-endian, it is stored last.

Check system byte order:

>>> import sys
>>> sys.byteorder
'little'