top of page
Hexa Decimal System
What is it?
-
At the very beginning of the computer development, there were many problems when working with binary numbers.
-
For this reason, a new numeric system, using 16 different symbols was established and called a hexadecimal numeric system.
-
It is comprised of ten digits we are used to (0, 1, 2, 3,... 9) and six letters of alphabet A, B, C, D, E, and F.
-
In Assembly Language programming, most assemblers require the first digit of a hexadecimal number to be 0 and place an "h" at the end of the number to denote the number base.
Base = 16 or 'H' or 'Hex'
It uses 16 letters { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F}
Example : AB12, 876F, FFFF, 83F6h
1 0 0 1 0 1 0 1 1 0 0 1 1 1 1 0
Binary
9
9
5
E
( 959E )
16
Conversation
-
Here are the 4-bit binary nos. with decimal and a binary value.
Converting Decimal to Hex :
-
Divide the decimal number by 16. Treat the division as an integer division.
-
Write down the remainder (in hexadecimal).
-
Divide the result again by 16. Treat the division as an integer division.
-
Repeat step 2 and 3 until the result is 0.
-
The hex value is the digit sequence of the remainders from the last to first.
10
16
(213) = ( ? )
Divide-by-16
Quotient
Remainder
Hex digit
213 / 16
13 / 16
​
13
0
5
13
Lower digit = 5
Second digit = D
(213) = (D5)
16
10
Decimal
Hexadecimal
Converting Hexadecimal to Decimal :
-
To convert from Hex to Decimal, multiply the value in each position by its hex weight and add each value.
(FACE) = ( ? )
10
16
Hexadecimal
Decimal
F A C E
( F * 16 )
( A * 16 )
( E * 16 )
( C * 16 )
3
2
0
1
+
+
+
=
61440 + 2560 + 192 + 14
=
= 64206
(64206)
10
Binary
( 15 * 4096 ) + ( 10 * 256 ) + ( 12 * 16 ) + ( 14 * 1 )
Converting Hexadecimal to Binary :
-
Each hexadecimal digit can be directly converted to its four-bit binary equivalent, using this table if necessary.
(FACE) = ( ? )
2
16
Hexadecimal
Binary
F A C E
1010
1100
1110
1111
(1111101011001110)
2
Binary
Application
-
Often used in computing as a compacter representation of binary (1 hex digit per 4 bits).
-
Easier for a human to read hexadecimal rather than binary.
-
. I.e. in HTML programming colors can be represented by a 6-digit hexadecimal number: FFFFFF represents white, 000000 represents black, and so on.
bottom of page