Introduction to IT By: Muhammed s. anwar

Number Systems A set of values used to represent different quantities is known as Number System A number system can be used to represent the number of students in a class The digital computer represents all kinds of data and information in binary numbers.  It includes audio, graphics, video, text and numbers

Some important number systems are as follows. Decimal number system Binary number system Octal number system Hexadecimal number system

Decimal number system The Decimal Number System consists of ten digits from 0 to 9. These digits can be used to represent any numeric value. The base of decimal number system is 10. It is the most widely used number system.

(1*1000)+(2*100)+(3*10)+(4*1) (1* 10 3 )+(2* 10 2 )+(3* 10 1 )+(4* 10 0 ) 1000+200+30+4 1234

Binary System Digital computer represents all kinds of data and information in the binary system.  Binary Number System consists of two digits 0 and 1. Each digit or bit in binary number system can be 0 or 1.  A combination of binary numbers may be used to represent different quantities like 1001.

Octal Number System Octal Number System consists of eight digits from 0 to 7. The base of octal system is 8. Each digit position in this system represents a power of 8. Any digit in this system is always less than 8. Octal number system is used as a shorthand representation of long binary numbers. The number 6418 is not valid in this number system as 8 is not a valid digit.

Hexadecimal number system The Hexadecimal Number System consists of 16 digits from 0 to 9 and A to F. The alphabets A to F represent decimal numbers from 10 to 15. The base of this number system is 16. Each digit position in hexadecimal system represents a power of 16. This number system provides shortcut method to represent long binary numbers

Decimal to Other Base System Step 1 - Divide the decimal number to be converted by the value of the new base. Step 2 - Get the remainder from Step 1 as the rightmost digit (least significant digit) of new base number. Step 3 - Divide the quotient of the previous divide by the new base. Step 4 - Record the remainder from Step 3 as the next digit (to the left) of the new base number. Repeat Steps 3 and 4, getting remainders from right to left, until the quotient becomes zero in Step 3. The last remainder thus obtained will be the most significant digit (MSD) of the new base number.

Decimal Number : 2910 = Binary Number : 111012.

Shortcut method - Binary to Octal Step 1 - Divide the binary digits into groups of three (starting from the right). Step 2 - Convert each group of three binary digits to one octal digit.

Octal to Binary

Binary to Hexadecimal

Hexadecimal for Binary