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Hexadecimal Numbers is a more complex system than using just binary or decimal and is mainly used when dealing with computers and memory address locations. By dividing a binary number up into groups of 4 bits, each group or set of 4 digits can now have a possible value of between “0000” (0) and “1111” ( 8+4+2+1 = 15 ) giving a total of 16 different number combinations from 0 to 15. Don’t forget that “0” is also a valid digit.

We remember from our first tutorial about Binary Numbers that a 4-bit group of digits is called a “nibble”. As 4-bits are also required to produce a hexadecimal number, a hex digit can also be thought of as a nibble, or half-a-byte. Thus two hexadecimal numbers are required to produce one full-byte ranging from 00 to FF.

Also, since 16 in the decimal system is the fourth power of 2 ( or 24 ), there is a direct relationship between the numbers 2 and 16 so one hex digit has a value equal to four binary digits so now q is equal to “16”.

Because of this relationship, four digits in a binary number can be represented with a single hexadecimal digit. This makes conversion between binary and hexadecimal numbers very easy, and hexadecimal can be used to write large binary numbers with much fewer digits.

The numbers 0 to 9 are still used as in the original decimal system, but the numbers from 10 to 15 are now represented by capital letters of the alphabet from A to F inclusive and the relationship between decimal, binary and hexadecimal is given below.

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Match the following. 1. (11) i0 2. (1001) 3. 0,1,2,3,...,7 4. 0,1,2,3