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### Chapter 2

Conversion

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

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

- Starting from the rightmost bit:
- Group each 4 bits together.
- Use the table.

- Hexadecimal to Binary

- Use the table.

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

Use the binary system as the intermediate system.

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