# What is Hexadecimal Numeral System?

Hexadecimal, base-16, or simply hex, is a numeral system with a radix, or base, of 16, usually written using the symbols 0–9 and A–F, or a–f. Its primary purpose is to represent the binary code in a format easier for humans to read, and acts as a form of shorthand, in which one hexadecimal digit stands in place of four binary bits.
For example, the decimal numeral 79, whose binary representation is 01001111, is 4F in hexadecimal (4 = 0100, F = 1111). IBM introduced the current hexadecimal system to the computing world; an earlier version, using the digits 0–9 and u–z, had been introduced in 1956, and had been used by the Bendix G-15 computer.
It is usually difficult for a person to look at a binary number and instantly recognize its magnitude. Unless you are quite experienced at using binary numbers, recognizing the relative magnitudes of 101011012 and 101001012 is not immediate (17310 is greater than 16510). Nor is it immediately apparent to us that 10011011012 equals 62110 without going through the process of calculating 512 + 64 + 32 + 8 + 4 + 1.
There is another problem:
we are prone to creating errors when writing or typing binary numbers. As a quick exercise, write the binary number 10010111111011010010001112 onto a sheet of paper. Did you make a mistake? Most people would have made at least one error.
To make the binary representation of numbers easier on us humans, there is a shorthand representation for binary values. It begins by partitioning a binary number into its nibbles starting at the least significant bit (LSB).
An example is shown below: Next, a symbol is used to represent each of the possible combinations of bits in a nibble. We start by numbering them with the decimal values equivalent to their binary value, i.e.: Table below presents the mapping between the sixteen patterns of 1’s and 0’s in a binary nibble and their corresponding decimal and hexadecimal (hex) values.
 Binary Decimal Hexadecimal 0000 0 0 0001 1 1 0010 2 2 0011 3 3 0100 4 4 0101 5 5 0110 6 6 0111 7 7 1000 8 8 1001 9 9 1010 10 A 1011 11 B 1100 12 C 1101 13 D 1110 14 E 1111 15 F
Another way to look at it is that hexadecimal counting is also similar decimal except that instead of having 10 numerals, it has sixteen. This is also referred to as a base-16 numbering system.
How do we convert binary to hexadecimal? Begin by dividing the binary number into its nibbles (if the number of bits is not divisible by 4, add leading zeros), then nibble-by-nibble use the table above to find the hexadecimal equivalent to each 4-bit pattern.
For example: Therefore, 10010111101101001001112 = 25ED2716. Notice the use of the subscript “16” to denote hexadecimal representation.

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