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Maths number conversion

Binary

There are 8 bits in a byte, 4 bits are called a nibble and work on a Base 16 or Hex, 3 bits work on Base 8 or Oct.

Converting from Base 10 (Decimal or normal) to any Base

Convert to binary divide by 2

Convert to octal divide by 8 (remember the answers will be to the power of 8)

Convert to hex divide by 16 (remember answers will be to the power of 16, also after 9 the numbers become a,b,c etc)

*After dividing the answers are to be read from the bottom up

Converting any Base to Base 10

Binary

Working backwards times the first number by one (the first is always one)

Times the second number by 2

Times the third number by 4

Times the forth number by 8 and so on

Octal

Times the first number by 1

Times the second by 8

Times the third by 320

Hexadecimal

Times the first number by 1

Times the second number by 16

Times the third number by 265

Powers

To figure out the powers when expanding and solving a problem

eg. 1100101

1×2(p6) 1×2(p5) 0x2(p4) 0x2(p3) 1×2(p2) 0x2(p1) 1×2(p0)

2 x 2 x 2 x 2 x 2 x 2

4   8   16   32   64

So 1×2(p6) = 64  1×2(p5) = 32 0x2=0 0x2=0 1×2(p2) = 4 0x2(p1) = 0 1×2(p0) = 1

64+32+4+1=101

**To the power of 0 always equals 1

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