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Presentation on Number System

Presentation on Number System. Types of Number System. Non-Positional number system Positional number system. Non-Positional Number System. Symbol represents the value regardless of its position. Difficult to perform arithmetic operation. For example:-

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Presentation on Number System

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  1. Presentation on Number System

  2. Types of Number System • Non-Positional number system • Positional number system

  3. Non-Positional Number System • Symbol represents the value regardless of its position. • Difficult to perform arithmetic operation. • For example:- I, II, III, IV, V, VI, VII, VIII, IX, X XI,XII, XIII, XIV, XV, XVI, XVII, XVIII, XIX, XX

  4. Positional Number System • Symbols represent different values depending upon the position. • The values of each digit is determined by:- - Digit itself - Position of the digit - Base of the number system

  5. Decimal number • The base is equal to 10 • Uses 10 different symbols.

  6. Continue… For example: (2*1000) + (5*100) + (8*10) + (6*1) =2000 + 500 + 80 + 6 =2586

  7. Bit • Binary digit 0 or 1 • Smallest possible unit of data • Work with a group of bits.

  8. Byte • Group of eight bits • Used to represent one character

  9. Binary Number System • The base is 2. • Each position represents a power of the base 2. • For example:-Conversion from 00111101 to decimal is-

  10. Octal Number System • The base is 8 • Largest single digit is 7 • For example:- decimal equivalent to the octal number 421 is 273

  11. Hexadecimal Number System • The base is 16 • Combination of 0-9 and A-F • For example:-Decimal equivalent to the hexadecimal number 1421 is 1057

  12. Decimal, binary and hexadecimal representations

  13. Determine the binary equivalent of 3610 Conversion of decimal representation to binary Remainder 0 0 1 0 0 1 Least Significant Bit (LSB) Most significant Bit (MSB)

  14. Continue… • Taking remainders in reverse order, we have 100100

  15. Conversion of binary representation to decimal = 16 + 8 + 0 + 2 + 0= 26

  16. Conversion of hexadecimal to binary • Each hexadecimal digit is equivalent to 4 binary digits. • For example:-binary equivalent to 2C :- 2 C = 0010 1100 2C = 001011002(in binary)

  17. Conversion binary to hexadecimal • The binary digits are arranged in groups of 4 starting from the right. • For example:-Convert 0011 0100 0110 to hexadecimal 0011 0100 0110 3 4 6 (001101000110) 2 = (346 )16

  18. Conversion of decimal representation to hexadecimal (5112)10 Remainder 8 = 8 15=F 3=3 1=1 Least significant bit (LSB) Most significant bit (MSB) (5112)10=(13F8)16

  19. Conversion of hexadecimal representation to decimal 163 162 161 160 4096 256 16 1 B6E 11*256 + 6*16 +14*1 = 2816 + 96 + 14 = (2926)10

  20. Conversion of octal representation to hexadecimal • Convert each octal digit to 3-bit binary form • Combine all the 3 bits binary form • Divide the binary numbers into the 4-bit binary form • Convert these 4 bits blocks into their respective hexadecimal symbols

  21. Continue… Example (2327)8 Combining 3-bit blocks we have 010011010111 Dividing of binary numbers into 4-bit binary blocks and converting these blocks into their respective hexadecimal symbols, we have: 0100 1101 0111 4 D 7

  22. Conclusion • Same procedure to convert decimal numbers to binary, octal & hexadecimal • Same procedure to convert from binary, octal & hexadecimal to decimal numbers

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