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

 

There’s 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 it’s a 10

Where you see an F. it’s a 15 and so on.

 

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

Is equal to                 B (11) times 16⁰  11 x 1 = 11

Plus                  5         times 16¹        5  x 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