Binary Decimal Octal andHexadecimal number systemsConversion of binary to decimal ( base 2 tobase 10)Example: convert (1000100)2 to decimal = 64 + 0 + 0+ 0 + 4 + 0 + 0 = (68)10Conversion of decimal to binary ( base 10 tobase 2)Example: convert (68)10 to binary 68/¸2 = 34 remainder is 0 34/ 2 = 17 remainder is 0 17 / 2 = 8 remainder is 1 8 / 2 = 4 remainder is 0 4 / 2 = 2 remainder is 0 2 / 2 = 1 remainder is 0 1 / 2 = 0 remainder is 1 Answer = 1 0 0 0 1 0 0

Note: the answer is read from bottom (MSB) totop (LSB) as 10001002 Conversion of decimal fraction to binary fraction•Instead of division , multiplication by 2 is carriedout and the integer part of the result is saved andplaced after the decimal point.The fractional part is again multiplied by 2 and theprocess repeated.Example: convert ( 0.68)10 to binary fraction.0.68 * 2 = 1.36 integer part is 10.36 * 2 = 0.72 integer part is 00.72 * 2 = 1.44 integer part is 10.44 * 2 = 0.88 integer part is 0 Answer = 0. 1 0 1 0…..Example: convert ( 68.68)10 to binary equivalent. Answer = 1 0 0 0 1 0 0 . 1 0 1 0….

Octal Number System•Base or radix 8 number system.•1 octal digit is equivalent to 3 bits.•Octal numbers are 0 to7. (see the chart down below)•Numbers are expressed as powers of 8.Conversion of octal to decimal( base 8 to base 10)Example: convert (632)8 to decimal = (6 x 82) + (3 x 81) + (2 x 80) = (6 x 64) + (3 x 8) + (2 x 1) = 384 + 24 + 2 = (410)10Conversion of decimal to octal ( base 10 tobase 8)

Example: convert (177)10 to octal 177 / 8 = 22 remainder is 1 22 / 8 = 2 remainder is 6 2 / 8 = 0 remainder is 2 Answer = 2 6 1Note: the answer is read from bottom to top as(261)8, the same as with the binary case.Conversion of decimal fraction to octal fraction iscarried out in the same manner as decimal to binaryexcept that now the multiplication is carried out by 8.

Decimal, Binary, Octal, and Hex NumbersDecimal Binary Octal Hexadecimal 0 0000 0 0 1 0001 1 1 2 0010 2 2 3 0011 3 3 4 0100 4 4 5 0101 5 5 6 0110 6 6 7 0111 7 7 8 1000 10 8 9 1001 11 9 10 1010 12 A 11 1011 13 B 12 1100 14 C 13 1101 15 D 14 1110 16 E 15 1111 17 F

Hexadecimal Number System•Base or radix 16 number system.•1 hex digit is equivalent to 4 bits.•Numbers are 0,1,2…..8,9, A, B, C, D, E, F. B is 11, E is 14•Numbers are expressed as powers of 16.•160 = 1, 161 = 16, 162 = 256, 163 = 4096, 164 =65536, …Conversion of hex to decimal ( base 16 to base10)Example: convert (F4C)16 to decimal = (F x 162) + (4 x 161) + (C x 160) = (15 x 256) + (4 x 16) + (12 x 1)

Conversion of decimal to hex ( base 10 to base16)Example: convert (4768)10 to hex. = 4768 / 16 = 298 remainder 0 = 298 / 16 = 18 remainder 10 (A) = 18 / 16 = 1 remainder 2 = 1 / 16 = 0 remainder 1 Answer: 1 2 A 0Note: the answer is read from bottom to top , sameas with the binary case. = 3840 + 64 + 12 + 0 = (3916)10

Conversion of binary to octal and hex•Conversion of binary numbers to octal and hexsimply requires grouping bits in the binary numbersinto groups of three bits for conversion to octal andinto groups of four bits for conversion to hex.•Groups are formed beginning with the LSB andprogressing to the MSB.•Thus, 11 100 1112 = 3478•11 100 010 101 010 010 0012 = 30252218•1110 01112 = E716•1 1000 1010 1000 01112 = 18A8716

# binay_octal_Hex

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**Description: ** binay_octal_Hex

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