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Number System

Number System. Non-positional Number Systems. Positional Number Systems. Number System. Non-positional Number Systems.

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Number System

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  1. Number System

  2. Non-positional Number Systems Positional Number Systems Number System

  3. Non-positional Number Systems • In early days, human being counted on fingers,. When ten fingers are not adequate, stones, pebbles, or sticks were used to indicate values. This method of counting uses anNon-positional Number Systems. • In this system symbols such as I for 1. II for 2, III for 3, IIII for 4 etc.

  4. Positional Number Systems • In a positional number system, there are only a few symbols called digits, and these symbols represent different values depending on the position they occupy in the number. The value of each digit in such a number is determined by three considerations: • the digit itself • the position of the digit in the number and • the base of the number system

  5. Decimal Number System Octal Number System Binary Number System Hexadecimal Number System Positional Number Systems

  6. Decimal Number System • The number system that we use in our day to day life is called theDecimal Number System. • We have ten symbols or digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) that can be used in this number system. Example: 123410

  7. Binary Number System • The binary number system is exactly like the decimal design except that the base is 2 instead of 10. • We have only two symbols or digits (0 and 1) that can be used in this number system Example: 10102

  8. Octal Number System • In the octal number system the base is 8. • So in this system there are eight symbols or digits : 0, 1, 2, 3, 4, 5, 6 and 7 Example: 2057 8

  9. Hexadecimal Number System • The Hexadecimal Number System is one with a base of 16. The base of 16suggests choices of 16 single character digits or symbols. Then first 10 digits are the digits of a decimal system 0, 1, 2, 3, 4, 5, 6, 7, 8, ,9. The remaining six digits are denoted by A, B,C, D, E, F representing the decimal values 10, 11, 12, 13, 14, 15 respectively. Example: 69BBA16

  10. Converting One Number System to Another • Converting to decimal from another base e.g. 1. 110012 = ?10 2. 4706 8 = ? 10 3. 1AC116 = ? 10 • 4052 6 =? 10 • 5. 11001 4 =? 10 • 6. 1AC113 =? 10

  11. Converting One Number System to Another • Converting from base 10 to a new base • (division- remainder technique) e.g. 1. 2510= ?2 2. 55210 =?8 3. 42810 =? 16

  12. Converting One Number System to Another • Converting from a base other than 10 to base other than 10 • Example: 1. 5456=?4 2. 101102=?8

  13. Shortcut method for Binary to Octal conversion E.g. 1011102=?8

  14. Shortcut method for octal to binary conversion Example: 5628=?2

  15. Shortcut method for binary to hexadecimal conversion Example: 110100112=?16

  16. Shortcut method for hexadecimal to binary conversion e.g. 1. 2AB16=?2 2. ABC16=?2

  17. Fractional Numbers • In the binary number system, fractional numbers are formed in the same general way as in the decimal system. Just as in the decimal system. e.g 1. 0.23510 and 68.5310 2. 0.101 and 10.01

  18. Fractional Numbers Q : Find the decimal equivalent of the binary number 110.101 and octal number 127.54 and hexadecimal number 2B.C4

  19. Memory Dump • Every computer stores numbers, letters, and other special characters in binary form. There are several occasions when computer professionals need to know the raw data contained in a computer memory. A commonly used way of doing this is to print out the memory contents on a printer. This printout is called a memory dump.

  20. What is a ‘bit’ in computer terminology • “Binary digit” is often to referred to by the common abbreviation bit. Hence, a bit in computer terminology means either a 0 or a 1. • A binary number consisting of ‘n’ bits is called n-bit number.

  21. ‘bit’ in computer terminology • How many different patterns of bits are possible with n-bits? Examples: 1. 6 bits 2. 7 bits 3. 8 bits

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