Monday, 6 February 2012

Number System

Decimal number system:
  • Base ‘10’
  • Digits used are 0-9
  • A decimal is represented by

A5A4A3A2A1A0. A-1A-2 = A5105+A4104+A3103+A2102+A1101+A0100+A-110-1+A-210-2
  • Example: (1023)10, (145.28)10 

Octal number system:
  • Base ‘8’
  • Digits used are 0-7
  • An octal number is represented by

A5A4A3A2A1A0. A-1A-2A-3 = A585+A484+A383+A282+A181+A080+A-18-1+A-28-2+A-38-3
  • Example: (754)8=7x82+5x81+4x80=15610

Hex-Decimal number system:
  • Base ‘16’
  • Digits used are 0-9, A-F
  • A hex-decimal number is represented by

A5A4A3A2A1A0. A-1A-2 = A5165+A4164+A3163+A2162+A1161+A0160+A-116-1+A-216-2
  • Example: AF16=Ax161+Fx160


Binary Number system:
  • Base ‘2’
  • Digits used are 0,1
  • A binary number is represented by

A5A4A3A2A1A0. A-1A-2A-3 = A525+A424+A323+A222+A121+A020+A-12-1+A-22-2+A-32-3
  • Example: 110.102=1x22+1x21+0x20+1x2-1+1x2-2

Number with any base:
let the base be ‘x’
(A2A1A0)x=A2x2+A1x1+A0x0        (decimal conversion)
Example: 2415=2x52+4x51+1x50


Back                                                              TOC                                                              Next



No comments:

Post a Comment