Prepared By:- Nisarg Amin

Topic:- Decimal & HexadecimalNumber System

Decimal Number System•The decimal number system is what we most commonly use. It is composed of 10 symbols-0,1,2,3,4 ,5,6, 7,8 and 9. Using these digits you can express any quantity it is also called thebase 10 system because it makes use of 10 digits. The number base is also called the radix.•The decimal system is a positional value system (also called the positional value system or the place value notation)in which the value of a digit depends on its position.

• For example, consider the whole number 256. • The rightmost digit position is the ones position (101).• The numeral in that position indicates how many ones are

present in the number. • Then next position to the left is the tens, then the hundreds,

ten thousands, and so on. • Each digit position has a weight that is ten times the weight

of the position to its right.

• The right most digit has the least positional value (weight), therefore, it is called the LeastSignificant Digit (LSD).

• The leftmost digit has the maximum positional value (weight), therefore, it is called the MostSignificant Digit (MSD).

• In the above example, 6 is the LSD and 2 is the MSD.

Hexadecimal Number System• The hexadecimal number system has 16 as the base

number. It has ten numeric digits 0, 1, 2, 3,4,5,6,7,8,9 and six letters A=10, B=11, C=12, D=13, E=14 & F=15.

• The hexadecimal system is also a positional numbering system. The value of a hexadecimal digit is expressed as the power of 16.

• As an example, consider a hexadecimal number with a fraction-- A65.C2, and the place values or positional values of each digit as a power of 16.

Conversion from Decimal to Binary, Octal and Hexadecimal

• A decimal number can be an integer, or a mixed number with an integer part and a fractional part.

• Two processes are required for converting a decimal number into any other number system, one for the integer part and the other for the fractional part.

Integer Part:-• This method involves repeatedly dividing the integer by

the new base until the quotient is zero and recording the remainder after each step of division.

• Finally, when no more division can occur, write down the remainders from bottom to top.

Fractional Part:-

• Multiply the fractional part by the new base.

• Record the integer part if there is one, else record 0.

• Repeat step 1 with the fractional part of the previous multiplication and then repeat step until the fractional part becomes 0. In case of infinite calculations, generally 3 digits are taken.

Decimal to hexadecimal•The conversion method of decimal to hexadecimal is the same as that of decimal to binary except that the base taken is 16 instead of 2.•For example, to convert 765.24510 to the hexadecimal equivalent, do the following:

Integer Part

16 765

16 47 - 13

16 2 - 15

0 - 2

0.245x 16

3.920x 16

14.720x 16

11.520

765.24510 = 2FD.3EB16

Fractional Part

Conversion of Hexadecimal to Decimal

• Similarly, to convert a hexadecimal number to its equivalent decimal number by add up the product of each digit value (0 to 9, A to F) with its positional value, as shown below:

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