Bits, Bytes, Hexadecimals, and ASCII

The fundamental unit of memory inside a computer is called a bit, which is a contraction of the words binary digit.
Thus, a bit is a binary digit; i.e., a 0 or 1.
Everything is stored on the computer in units of bits.
Because most data communications is serial in nature, most data communication and networking services indicate capacity in unit of bits per second; e.g., Ethernet operates at 10 million bits/sec (Mbps).
Some communication schemes, such as Fibre Channel, are parallel and describe capacity in terms of bytes/sec. but that is less common.

Memory combines individual bits into larger units.
Byte is equivalent to 8 bits, also called an octet.
Computer media, including memory and disk drives, generally report their size in terms of bytes, such as 256 MB of RAM or a 120 GB hard drive.
A byte, historically, is a computer architecture term that refers to a memory storage of a single character.

A nibble is half of a byte, or 4 bits: e.g. 1011
There are two nibbles per byte and a single nibble may be expressed as a single hex digit.
This term is merely a convenience; nibbles are not used to express memory capacity, size, or speed.

Simplifies notation of bit patterns.
Much better alternative, compared to binary number notation.
Simplifies notation of long binary strings, such as entire blocks of computer memory.
Hexadecimal notation is used mainly for human convinience.
Hexadecimal notation represents numbers
of base 16, calculated as
- h₃*16³ + h₂*16² + h₁*16¹ + h₀*16⁰
where h₃, h₂, h₁, and h₀ are values from the Hexadecimal column of the table.

Decimal	Hexadecimal	Octal	Binary
`0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15`	`0 1 2 3 4 5 6 7 8 9 A B C D E F`	`000 001 002 003 004 005 006 007 010 011 012 013 014 015 016 017`	`0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 1111`

Positive integers are represented in a straightfoward positional scheme.
Corresponding negative integer binary representations are calculated by the following steps:
1. Invert each bit of the positive number.
2. Add 1.
3. If there is a carry over from the highest bit, ignore it.
The same steps are used to go from negative back to positive number.

8 bit two's complement:

Binary value	Two's complement interpretation	Unsigned interpretation
00000000	0	0
00000001	1	1
...	...	...
01111110	126	126
01111111	127	127
10000000	-128	128
10000001	-127	129
10000010	-126	130
...	...	...
11111110	-2	254
11111111	-1	255

An 8-bit byte can accommodate up to 2⁸, or 256, characters.
ASCII is the American Standard Code for Information Interchange, an American National Standard computer character code. ASCII is an 8-bit code with 256 characters:

See also: http://ascii-table.com/ interactive ASCII decoder