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Base ‘b’ number

Base ‘b’ number. In general a number system can have any base b the digit used are 0, 1, … , b-1 The weight of i th place is b i The conversion formula from base b into decimal number is Commonly used base are 2, 3, 8, 10, 16,. for i = 0 to n – 1 for an n digit quantity.

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Base ‘b’ number

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  1. Base ‘b’ number • In general a number system can have any base b • the digit used are 0, 1, … , b-1 • The weight of ith place is bi • The conversion formula from base b into decimal number is • Commonly used base are 2, 3, 8, 10, 16, ... for i = 0 to n – 1 for an n digit quantity

  2. Bases 2, 8, and 16 are related

  3. Conversion • From binary to octal • make groups of 3 bits from right to left 01 110 1102 1668 • From octal to binary • make each digit as 3 bits sequence 2768 010 111 1102 • From binary to hexadecimal • make groups of 4 bits from right to left 0111 01102 7616 • From hexadecimal to binary • make each digit as 4 bits sequence 3716 0011 01112

  4. More on Conversion • Convert from base b1 to decimal • Convert from decimal to base b2 • Direct conversion from base b1 and base b2 • we will not pursue this anymore • Decimal to Hexadecimal • Divide by 16 recursively and collect digit from right to left from the remainders. • Example 347110 = D8F16 • 3471 divided by 16 gives 216, remains 15 (F) • 216 divided by 16 gives 13, remains 8 (8) • 13 divided by 16 gives 0, remain 13 (D)

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