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: d 31 d d 2 d 1 d 0 is a 32 digit number value = d 31 x B 31 + d 30 x B d 2 x B 2 + d 1 x B 1 + d 0 x B 0

Decimal Numbers: Base 10 Base or Radix is 10 Digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 Example: = 4x x x10 0 = = 412

Binary Numbers: Base 2 Base or Radix is 2 Digits: 0, 1 Example: = 1x x x2 0 = = 5

Octal Numbers: Base 8 Base or Radix is 8 Digits: 0, 1, 2, 3, 4, 5, 6, 7 Example: = 1x x x8 0 = = 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: = 1x x16 0 = = 18

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

Decimal to Binary

Conversion of to Binary =

Binary to decimal conversion X2 0 = 1 0X2 1 = 0 0X2 2 = 0 1X2 3 = 8 1X2 4 =

Decimal to Octal

Conversion of to Octal =175 8

Octal to decimal conversion 175 5X8 0 = 5 7X8 1 = 56 1X8 2 = =

Conversion of to Octal =124 8

Octal to decimal conversion 124 4X8 0 = 4 2X8 1 = 16 1X8 2 = = 84 10

Decimal to Hexa

Conversion of to Hexadecimal =1C2 16

Hexa to decimal conversion 1C2 2X16 0 = 2 12X16 1 = 192 1X16 2 = C2 16 =

Conversion of to Hexadecimal =181 16

Hexa to decimal conversion 181 1X16 0 = 1 8X16 1 = 128 1X16 2 = =

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

BINARY  OCTAL OCTAL – BASE 8 = DIGIT BINARY NUMBER Example:  OCTAL =31 8

Example:  OCTAL =163 8

BINARY  HEXA HEXA – BASE 16 = DIGIT BINARY NUMBER Example:  HEXA =19 16

Example:  OCTAL =163 8

OCTAL  HEXA OCTAL  BINARY  HEXA Example:31 8  HEXA =19 16

HEXA  OCTAL Example: 1BD  OCTAL 1 B D BD = 675 8

Conversion of to Binary =

0.125 X 2 = X 2 = X 2 = =

Binary to decimal conversion X2 -3 = X2 -2 = 0 0X2 -1 = 0 1X2 0 = 1 0X2 1 = 0 0X2 2 = 0 1X2 3 = 8 1X2 4 =

Conversion of to Octal =124 8

0.250 X 8 = =

Octal to decimal conversion X8 -1 = X8 0 = 1 2X8 1 = 0 1X8 2 =