Hexadecimal system is a 16-base number system whose digits are the possible remainders of division by 16. The digits used for Hexadecimal representation are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E and F. As a single digit cannot consist of two digits, the remainders 10, 11, 12, 13, 14 and 15 are correspondingly represented by the upper case letters A, B, C, D, E and F.

It is often required to convert Hexadecimal representation to Decimal form and vice versa.

The stuff on this page gives the method for such conversions.

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The suffix 16 at the end of a number indicates that a hexadecimal number. To convert a hexadecimal number into decimal form, each digit is multiplied by its place value and the sum of all such products gives the decimal number required.

Here the place values in a hexadecimal representation are powers of 16, 16

The power is incremented by 1 as the places are counted from right to left.

F2A5 = 15 x 16

= 15 x 4096 + 2 x 256 + 160 + 5

= 61,440 + 512 + 160 + 5

= 62,117

The hexadecimal digits required are got by successive division of the number and the quotients by 16. This can be achieved in two ways.

Let us consider the decimal number 1843

Divide 1843 by 16. We get 1843 = 16 x 115 + 3. This means the quotient is 115 and the remainder is 3.

Digit in Units place =

Divide the quotient got in the division again by 16. We get 115 = 16 x 7 + 3. Quotient = 7 and remainder = 3

Digit in 16's place =

As the quotient in the last division is less than 7, the division by 16 cannot be continued and 7 is taken as the next digit.

Digit in 16

Thus

The number is first divided by the highest power of 16 possible. The quotient is taken as the digit corresponding to that place value and the division is continued with the remainder by a lesser power of 16.

Consider the decimal number 5287

16

Divide 5,287 by 4096 . 5,287 = 4096 x 1 + 1191.

Digit in 16

Divide the remainder 1191 by the next lower power of 16, that is 16

1191 = 256 x 4 + 167

Digit in 16

Divide the remainder 167 by 16. 169 = 16 x 10 + 7

Digit in 16's place =

Digit in Unit's place =

Thus