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HEXADECIMAL

 

Hexadecimal number system works just like the decimal numbering system except we use powers of base 16 instead of powers of base 10.

HEXADECIMAL

4,096††† 256††† 16†††† 1

163†††††† 162†† 161†††† 160

1†††††††† 1††††††† 1††††††† 1

 

Binary uses two symbols †††††††††††† 0 and 1

Decimal uses ten symbols††††††††††† 0,1,2,3,4,5,6,7,8, & 9

Hexadecimal uses 16 symbols†††††† 0 through 15

 

Thereís a problem in writing hex with values over 9 in the number

How would you read this hex number?††††††††††† 12510

Is it 1 then 2 or is it a value or 12?

Does it end in 0 or in 10?

In order to distinguish one place value from the others
we use a code for the two digit values of †††††††††††††† 10, 11, 12, 13, 14, & 15.

We call them††††††††††††††††††††††††††††††††††††† †††††††††††††† A,B,C,†† D,†† E, &F

So where you see an A itís a 10

Where you see an F. itís a 15 and so on.

 

So the hex number 5Bh (little h means hexadecimal)

Is equal to ††††††††††††††† B (11) times 16011 x 1 = 11

Plus††††††††††††††††† 5†††††††† times 161††††††† 5x 16 = 80

Equals†††††††††††††††††††††††††††††††††††††††††††††† ††† 91 in decimal

 

 

Most often we use hexadecimal as a shorthand for binary.

0000 in binary is†††††††† 0 in hex

0001 in binary is†††††††† 1 in hex

0010†††††††††††††††††††††††† 2 in hex

1000†††††††††††††††††††††††† 8 in hex
1010†††††††††††††††††††††††† 10 or A in hex

1100†††††††††††††††††††††††† (8+4) 12 or C in hex

1111†††††††††††††††††††††††† (8+4+2+1) 15 or F in hex

 

One hex digit represents four binary digits

Hex number †††††††††††††††††††††††† binary

Ah†††††††††††††††††††††††††††† 1010

AFh†††††††††††††††††††††††††† 10101111 in binary

5Ch†††††††††††††††††††††††††† 01011010 in binary

 


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