NUMBER SYSTEM

Number System Number Base B => B symbols Base 16(Hexa):0, 1,……9, A ,…, E, F Base 10 (Decimal): 0, 1, 2,……, 7, 8, 9 Base 8(Octal): 0, 1, 2, 3, 4, 5, 6, 7 Base 2 (Binary): 0, 1

Number System (cont) Number representation: d31d30 ... d2d1d0 is a 32 digit number value = d31x B31 + d30 x B30 + ... + d2 x B2 + d1 x B1 + d0 x B0

Decimal Numbers: Base 10 Base or Radix is 10 Digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 Example: 41210 = 4x102 + 1x101 + 2x100 = 400 + 10 +2 = 412

Binary Numbers: Base 2 Base or Radix is 2 Digits: 0, 1 Example: 1012 = 1x22 + 0x21 + 1x20 = 4 + 0 +1 = 5

Octal Numbers: Base 8 Base or Radix is 8 Digits: 0, 1, 2, 3, 4, 5, 6, 7 Example: 1238 = 1x82 + 2x81 + 3x80 = 64 + 16 +3 = 83

Hexadecimal Numbers: Base 16 Digits: 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F: A  10 B  11 C  12 D  13 E  14 F  15 Example: 1216 = 1x161 + 2x160 = 16 +2 = 18

Conversions Decimal to Base N Base N to Decimal Successive Division by N (Remainder Method) Multiplication with power of N

Decimal to Binary

Conversion of 2510 to Binary 2 25 2 12 -1 2 6 - 0 2 3 - 0 1 - 1 2510=110012

Binary to decimal conversion 11001 1X20 = 1 0X21 = 0 0X22 = 0 1X23 = 8 1X24 = 16 2510

Decimal to Octal

Conversion of 12510 to Octal 8 125 8 15 - 5 1 - 7 12510=1758

Octal to decimal conversion 175 5X80 = 5 7X81 = 56 1X82 = 64 125 1758 = 12510

Conversion of 8410 to Octal 8 84 8 10 - 4 1 - 2 8410=1248

Octal to decimal conversion 124 4X80 = 4 2X81 = 16 1X82 = 64 84 1248 = 8410

Decimal to Hexa

Conversion of 45010 to Hexadecimal 16 450 16 28 - 2 1 - 12 45010=1C216

Hexa to decimal conversion 450 1C216 = 45010

Conversion of 38510 to Hexadecimal 16 385 16 24 - 1 1 - 8 38510=18116

Hexa to decimal conversion 181 1X160 = 1 8X161 = 128 1X162 = 256 385 18116 = 38510

Other Conversions BINARYOCTAL BINARYHEXA OCTALHEXA etc,.

BINARYOCTAL OCTAL – BASE 8 = 23 3 DIGIT BINARY NUMBER Example:110012  OCTAL 11 001 011 001 3 1 110012=318

Example:11100112  OCTAL 1 110 011 001 110 011 1 6 3 11100112=1638

BINARYHEXA HEXA – BASE 16 = 24 4 DIGIT BINARY NUMBER Example:110012  HEXA 1 1001 0001 1001 1 9 110012=1916

Example:11100112  OCTAL 1 110 011 001 110 011 1 6 3 11100112=1638

OCTALHEXA OCTALBINARYHEXA Example:318  HEXA 3 1 011 001 0001 1001 1 9 318=1916

HEXA  OCTAL Example: 1BD  OCTAL 1 B D 0001 1011 1101 000 110 111 101 0 6 7 5 1BD = 6758

Conversion of 25.12510 to Binary 2 25 2 12 -1 2 6 - 0 2 3 - 0 1 - 1 2510=110012

0.125 X 2 = 0.250 0.250 X 2 = 0.5 0.5 X 2 = 1.0 25.12510 = 11001.0012

Binary to decimal conversion 11001.001 1X2-3 = 0.125 0X2-2 = 0 0X2-1 = 0 1X20 = 1 0X21 = 0 0X22 = 0 1X23 = 8 1X24 = 16 25.12510

Conversion of 84.25010 to Octal 8 84 8 10 - 4 1 - 2 8410=1248

0.250 X 8 = 2.000 25.12310 = 124.28

Octal to decimal conversion 124.2 2X8-1 = 0.25 4X80 = 1 2X81 = 0 1X82 = 0 25.25010

ASSIGNMENT

DECIMAL TO BINARY 43 79 107 241 476

DECIMAL TO OCTAL 39 152 284 758 2534

DECIMAL TO HEXA 75 826 3128 7359 4756

DECIMAL TO OTHER 63 BASE4 279 BASE6 161 BASE7

BINARY  OCTAL,HEXA 1010101 11010101011 111010110111 1011110111 101000101

OCTAL  HEXA 473 1235 724 5774 4625

75.12510 BASE2 356.52310 OCTAL 527.4210 HEXA