We remember from our first tutorial about Binary Numbers that a 4-bit group of digits is called a “nibble” and 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. Don’t forget that “ 0” is also a valid digit. 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. 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.
In the everyday use of the decimal numbering system we use groups of three digits or 000’s from the right hand side to make a very large number such as a million or trillion, easier for us to understand and the same is also true in digital systems.
For example, the following group of binary digits 1101 0101 1100 1111 2 are much easier to read and understand than 1101010111001111 2 when they are all bunched up together. Then in the Hexadecimal Numbering System we use the numbers from 0 to 9 and the capital letters A to F to represent its Binary or Decimal number equivalent, starting with the least significant digit at the right hand side.Īs we have just said, binary strings can be quite long and difficult to read, but we can make life easier by splitting these large binary numbers up into even groups to make them much easier to write down and understand. , fifteen are replaced with capital letters of A, B, C, D, E and F respectively. To get around this tricky problem hexadecimal numbers that identify the values of ten, eleven. For example, if we write 10 in hexadecimal, do we mean the decimal number ten, or the binary number of two (1 + 0).
However, there is a potential problem with using this method of digit notation caused by the fact that the decimal numerals of 10, 11, 12, 13, 14 and 15 are normally written using two adjacent symbols. In other words, there are 16 possible digit symbols. The “Hexadecimal” or simply “Hex” numbering system uses the Base of 16 system and are a popular choice for representing long binary values because their format is quite compact and much easier to understand compared to the long binary strings of 1’s and 0’s.īeing a Base-16 system, the hexadecimal numbering system therefore uses 16 (sixteen) different digits with a combination of numbers from 0 through to 15.