Encoding Schemes and Number System

ASCII character capacity (7-bit): 2^7 = 128

ISCII character capacity (8-bit): 2^8 = 256

UNICODE gives a unique number for every character

Decimal positional value computation: 1 × 10^2 + 2 × 10^1 + 3 × 10^0 + 4 × 10^{-1} + 5 × 10^{-2} = (123.45)_{10}

Octal base in terms of 2: 8 = 2^3

Hexadecimal base in terms of 2: 16 = 2^4

Binary to Decimal example: 1×2^3 + 1×2^2 + 0×2^1 + 1×2^0 = 8+4+0+1 = (13)_{10}

Octal to Decimal example: 2×8^2 + 5×8^1 + 7×8^0 = 128+40+7 = (175)_{10}

Decimal to other base: divide by base, note remainders, write remainders in reverse order

Fractional decimal to other base: repeatedly multiply by base until fraction becomes 0 or repeats

Binary to octal: group 3 bits at a time

Binary to hexadecimal: group 4 bits at a time

(10101100)2 = (254)8

(705)8 = (111000101)2

(0110101100)2 = (1AC)16

(23D)16 = (001000111101)2