NETWORK Notes 2: number system, symbols, conversion

Number system: a method of representing a number system with a fixed set of symbols and unified rules.

Digital: different digital symbols that represent the size of a basic value in a number system.

For example, there are two digits in binary system: 0, 1.

Octal has 8 digits: 0, 1, 2, 3, 4, 5, 6, 7

The decimal system has 10 digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9

Hexadecimal has 16 digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F

Cardinality: the number of digits used in the digital system.

For example, the cardinality of binary is 2

The base of octal is 8

The base of the decimal system is 10

The hexadecimal base is 16

Bit weight: the size of the value represented by 1 on a bit in the number system.

For example, the bit weight of binary 101 1 is 4, the bit weight of 0 is 2, the bit weight of 1 is 1

The bit weight of octal 101 1 is 64, the bit weight of 0 is 8, and the bit weight of 1 is 1

The bit weight of decimal 101 1 is 100, 0 is 10, and 1 is 1.

The bit weight of hexadecimal 101 1 is 256, the bit weight of 0 is 16, and the bit weight of 1 is 1.

Number system symbol: binary B (binary) for example: (101) 2 or 101B

Octal O (octal) (101) 8 or 1010

Decimal D (decimal) (101) 10 or 101D

Hexadecimal H (hexadecimal) (101) 16 or 101H

Binary: every two into one

(101) 2 "1x22" 0x21 "1x20 = (5) 10

Octal: every eight into one

(101) 81x820x811x80 = (65) 10

Decimal system: every ten into one

(101) 10 "1x102" 0x101 "1x100 = (101) 10

Hexadecimal: every hexadecimal

(101) 16 "1x162" 0x161" 1x160 = (257) 10

(10110101.101) 2 = (1x27+0x26+1x25+1x24+0x23+1x22+0x21+1x20+1x2-1+0x2-2+1x2-3) 10

= 181.625