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Chapter 2. Conversion. Any base to decimal. ( S k-1 … S 2 S 1 S 0 . S -1 S -2 …S -L ) b. S k-1 x b k-1 + … + S 2 X b 2 + S 1 X b 1 + S 0 X b 0. S -1 x b -1 + S -2 X b -2 + … + S -L X b -L. n = . +. Decimal to any base. Convert integral part. Convert fractional part.

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Chapter 2

Chapter 2

Conversion


Any base to decimal
Any base to decimal

( Sk-1 … S2S1S0.S-1S-2…S-L ) b

Sk-1 x bk-1+ … + S2 X b2+ S1X b1+ S0X b0

S-1 x b-1+ S-2 X b-2+ … + S-LX b-L

n =

+


Decimal to any base
Decimal to any base

Convert integral part

Convert fractional part

In each step:

- Keep the Remainder in the Destination.

- Stop when Quotient =0

In each step:

- Keep the Integral part in the Destination.

- Stop when Fractional part =0OR destination digits are enough


Binary to hexadecimal
Binary to Hexadecimal

  • Starting from the rightmost bit:

  • Group each 4 bits together.

  • Use the table.

  • Hexadecimal to Binary

- Use the table.


Binary to octal
Binary to Octal

  • Starting from the rightmost bit:

  • Group each 3 bits together.

  • Use the table.

  • Octal to Binary

- Use the table.


Octal to hexadecimal or vise versa
Octal to Hexadecimal or vise versa

Use the binary system as the intermediate system.


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