Shashank Srivastavhshsusubeueheuehm.pptx

Number system mathematics

1. BETHEL ACADEMY Submitted To :- TANYA JAISWAL MAAM Submitted by :- SHASHANK SRIVASTAVA CLASS 7 TH

2. NUMBER SYSTEM

3. S.no. Description Slide no. 1. Introduction to Number System 3 2. Basic facts 4 3. Decimal Number System 5-6 4. Binary Number System 7 5. Conversions 8-9 6. Octal Number System 10 7. Hexadecimal Number System 11 8. Table 12 9. Uses in Computer System 13 10. Sources 14 INDEX

4. NUMBER SYSTEM A number system defines how a number can be represented using distinct symbols. A number can be represented differently in different systems. Many number systems were introduced with the passage of time, like: Decimal number system Binary number system Octal number system Hexadecimal number system

5. A unit of information expressed as either a 0 or 1 in binary notation. BIT BYTE A group of binary digits or bits (usually eight) operated on as a unit. A byte is considered as a unit of memory size. BASE (RADIX) The base is the number of digits used in it. The larger the base, the more numerals are required. Decimal- Base 10 . Binary- Base 2 Octal- Base 8 . Hexadecimal- Base 16

6. Decimal Sy stem The need for counting has paved the path to introduce decimal number system in which 10 digits 0,1,2,3…9 are used to form any number. Most of our arithmetic operations are performed with decimal numbers. The prefix ‘ deci ’ stands for 10. The decimal number system is a base 10 number system. Each number can be used individually or they can be grouped to form a numeric value. Example- 52, 16.83, -243 etc. The value of each digit in a number depends upon the following: The face value of the digits The base of the number system

7. BINARY NUMBER SYSTEM The prefix ‘bi’ stands for 2. The binary number system consists of 2 digits 0 and 1. Since this system uses two digits it has a base: 2. All digital computers use this number system and convert the data input from the decimal format into its binary equivalent. Since the computer is made up of electronic components; it can have only two states, either on (1) or off (0). So the data given to the computer is converted into binary form because a computer understands only binary language. Example- (987) 10

8. Conversion of decimal number into binary The rules are: Divide the given decimal number with the base 2. Write down their remainder and divide the quotient again by 2. Repeat the step 2 till the quotient is 0. Example-

9. Conversion of binary into decimal n o. The rules are: Multiply each binary number with 2 having the power 0 for unitary position, starting from the extreme right digit. Increase the power one by one keeping the base fixed as 2. Sum up all the products to get the decimal number. (11010110) 2 = (214) 10 Example-

10. OCTAL NUMBER SYSTEM Octal (base 8) was previously a popular choice for representing digital circuit numbers in a form that is more compact than binary. The octal number system consists of 8 digits i.e. 0 to 7 with the base 8. 1 octal digit is equivalent to 3 bits. Examples: 27 8  = 2×8 1 +7×8 0  = 16+7 = 23 30 8  = 3×8 1 +0×8 0  = 24 4307 8  = 4×8 3 +3×8 2 +0×8 1 +7×8 = 2247

11. HEXADECIMAL No. SYSTEM The prefix ‘ hexa ’ stands for 6 and the prefix ‘ deci ’ stands for 10. This number system contains 16 systems and therefore has the base 16. It uses the digits (0-9) and (A-F). Numbers are 0, 1, 2…8, 9, A, B, C, D, E, F. B is 11, E is 14. 1 Hex digit is equal to 4 bits. Each place value in a hexadecimal number is a power of 16.

12. TABLE

13. Uses in computer system A switch is just used to turn ON or turn OFF any desired device… using the concept binary system. Electronic Circuitry uses the octal system and hexadecimal system. Decimal number system uses basic calculation and complex calculation in daily life.

14. Sources www.easytechtips24.com/ www.aqua-calc.com/ www.rapidtables.com/ IT PATH School Book Class 7 www.wikipedia.org/

15. THANK YOU