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 BINARYOCTAL BINARYHEXA OCTALHEXA etc,.
BINARYOCTAL 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
BINARYHEXA 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
OCTALHEXA OCTALBINARYHEXA 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