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Decimal number system
The document discusses decimal and hexadecimal number systems. The decimal system uses 10 symbols (0-9) in a positional notation where the value of each digit depends on its position. Hexadecimal uses 16 symbols (0-9 plus A-F) with a base of 16. To convert between number systems, the integer and fractional parts are converted separately by repeated division or multiplication by the new base. For example, to convert decimal 765.245 to hexadecimal, 765 divides into 16 with remainder 13 and fractional part 0.245 is multiplied by 16 repeatedly.
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This slide introduces the presentation by Nisarg Amin on Decimal and Hexadecimal number systems.
Describes the decimal system, base 10, consisting of digits 0-9. Highlights its positional value structure.
Explains how the value of a whole number like 256 is determined by the position of its digits.
Defines Least Significant Digit (LSD) and Most Significant Digit (MSD) in the example of the number 256.
Introduces hexadecimal system as base 16, using digits 0-9 and letters A-F, with positional notation.
Outlines the methods required for converting decimal numbers (integer and fractional) to other bases.
Details the steps for converting the fractional part of a decimal number to a new base.
Illustrates converting decimal to hexadecimal using the method similar to decimal to binary conversion.
Explains conversion from hexadecimal back to decimal by calculating the product of digit values.
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Decimal number system
- 1. Prepared By:- NisargAmin Topic:- Decimal & Hexadecimal Number System
- 2. Decimal Number System •Thedecimal 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 the base 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.
- 3. • 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.
- 4. • The rightmost digit has the least positional value (weight), therefore, it is called the Least Significant Digit (LSD). • The leftmost digit has the maximum positional value (weight), therefore, it is called the Most Significant Digit (MSD). • In the above example, 6 is the LSD and 2 is the MSD.
- 5. 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.
- 6. Conversion from Decimalto 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.
- 7. Fractional Part:- • Multiplythe 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.
- 8. Decimal to hexadecimal •Theconversion 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 0.245 x 16 3.920 x 16 14.720 x 16 11.520 765.24510 = 2FD.3EB16 Fractional Part
- 9. Conversion of Hexadecimalto 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: