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Binary No. System

Home > PowerPoint Slides > Binary No. System
Published in: Basic Computer
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What are Binary Nos. Convertion of Binary No. System to Decimal No. System and vice versa. Hexagon DecimalNno. System and Octadecimal No. System.

Anita Y / Gurgaon

7 years of teaching experience

Qualification: Masters in physics

Teaches: Mathematics, Physics

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  1. BINARY NO. SYSTEM By-Anita Yadav
  2. CONTENTS Introduction Decimal Number System Binary Number System Why Binary? Octal Number System Hexadecimal Number System Relationship between Hexadecimal, Octal, Decimal, and Binary Number Conversions
  3. Decimal Number System It consist of ten digit i.e. 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 with the base 10. Each number can be used individually or they can be grouped to form a numeric value as etc.
  4. BINARY NUMBER SYSTEM The Binary Number System consist of only two digits— O and 1. Since this system use two digits, it has the base 2. All digital computer use this number system and convert the data input from the decimal format into its binary equivalent.
  5. why Binary? Since the computer is made up of electronic components; it can have only two states, either on(l) Off(0) The data which is given to the computer is converted into binary form because a computer understand only binary language. It further converts the binary results into their decimal equivalents for output.
  6. Octal Number System — In the Octal Number System it consist of 8 digits i.e. 0, 1, 2, 3, 4, 5, 6, 7 with a base 8. The sequence of octal number goes as 0, 1, 2, 3, 4, 5, 6, 7, 10, 11, 12, 13, 14, 15, 16, 17, 20, 21, 22 , .. ...as go on. See each successive number after 7 is a combination of two or more unique symbols of octal system.
  7. Hexadecimal Number System The Hexadecimal system use base 16. It has 16 possible digit symbol. It use the digit 0 through 9 plus the letters A, B, C, D, E, and F as the 16 digit symbols.
  8. Relationship between Hexadecimal, Octal, Decimal, and Binary Hexadeci Octal Decimal Binary mal 2 3 4 5 6 7 8 9 c D 1 2 3 4 5 6 7 10 11 12 13 14 15 16 17 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 Notice that each hexadecimal digit represent a group of four binary digit. It Is important to remember that Hex(Abbreviation for Hexadecimal) digit A through F are equivalent to the decimal value 10 through 15.
  9. NUMBER CONVFRSIONS
  10. Decimal-to-Binary Conversion The method of converting Decimal to binary is repeated-division method. For conversion follow the rules: 1. 2. 3. Divide the given decimal number with the base 2. Write down the remainder and divide the quotient by 2. Repeat step 2 till the quotient is zero.
  11. Convert 20010 to Binary Number 2 2 2 2 2 2 2 2 200 100 50 25 12 6 3 Remainders 0 Write 1 order 1 Reading the remainders from the bottom to top, the result is LSB in this MSB 20010 — 110010002
  12. Binary-to-Decimal Conversion To convert a binary number follow the steps: 1. 2. 3. Multiply each binary number with 2 having the power 0 for last position, starting from the right digit. Increase the power one by one, with base as 2. Sum up all the products to get decimal number.
  13. Convert 1100010012 to Decimal Number 1100010012= 1 x 28 +1 x 27 + ox 26 + ox 25+0 x 24+1 x 23+ ox 22+0 x 21 1 x 20 = 256 + 128 + O + 0 + 0 + 8 + 0 + 0 + 1 = 393 Thus, 1100010012 = 393 10
  14. Decimal-to-Octal The method of converting Decimal to Octal is repeated-division method. For conversion follow the rules: 1. 2. 3. Divide the given decimal number with the base 8, Write down the remainder and divide the quotient by 8, Repeat step 2 till the quotient is zero.
  15. Convert 50010 to Octal Number 8 8 8 266 33 4 o Remainders 2 1 4 MSB LSB Reading the remainders from the bottom to top, the result is = 4128 26610
  16. Octal-to-Decimal Conversion To convert a octal number follow the steps: 1. 2. 3. Multiply each Octal number with 8 having the power 0 for last position, starting from the right digit. Increase the power one by one, with base as 8. Sum up all the products to get decimal number.
  17. Convert (372)8 to Decimal Number 3728 = 3 x 82+7 x 81+2X80 = 3 X 64 + 7 X 8 + 2 X I = 192 + 56 +2 = 25010 Thus, 3728 250 So, an octal number can be easily converted to its decimal equivalent by multiplying each octal digit by its position weight.
  18. Octal-to-Binary Conversion The conversion from octal to binary is performed by converting each octal digit to its 3-bit binary equivalent. The eight possible digits are converted as indicated below: Octal Digit Binary Equivalent 000 001 010 011 100 101 110 111 using tnese conversions, any octal numoer IS converted to binary by individually converting each digit.
  19. Convert 54318 to Binary Number We convert 54318 to binary using 3 bits for each octal digit as follows: 5 4 3 1 001 101 100 011 Thus, 54318 = 1011000110012
  20. Binary-to-Octal Conversion Converting from binary integers to octal integers is simply the reverse of the foregoing process. Firstly you have to do is: 1. Group the binary integer into 3-bits starting at the Least Significant Bit(LSB). 2. If unable to form group then, add one or two Os. 3. Each group Is converted to its octal equivalent. It illustrated below for bina number 11010110 Thus, 110101102 326 8
  21. Decimal-to-Hexadecimal Conversion The method of converting Decimal to Hexadecimal is repeated-division method. For conversion follow the rules: 1. 2. 3. Divide the given decimal number with the base 16. Write down the remainder and divide the quotient by 16. Repeat step 2 till the quotient is zero.
  22. Convert 42310 to Hexadecimal 16 16 16 423 26 1 O Remainders 7 1 LSB MSB Reading the remainders from the bottom to top, the result is 42310 = IA7 16 Note: Any remainder greater than 9 are represented by letters A through F.
  23. Hexadecimal-to-Decimal Conversion To convert a Hexadecimal number follow the steps: 1. 2. 3. Multiply each hexadecimal number with 16 having the power 0 for last position, starting from the right digit. Increase the power one by one, with base as 16. Sum up all the products to get decimal number.
  24. Convert 2AF16 to Decimal Number 2AF16 = 2 x 162 + 10 x 161 + 15 x 160 = 512 + 160 + 15 = 68710 Thus, 2AF16 68710
  25. Binary-to-Hexadecimal Conversion Converting from binary integers to hexadecimal integers is simple. Firstly you have to do is: 1. Group the binary integer into 4-bits starting at the Least Significant Bit(LSB). 2. If unable to form group then, add one or two Os. 3. Each group Is converted to its Hexadecimal equivalent. It illustr 01 OW for be mber 1 010 010 01 B 2 Thus, 10101110102 = 2BA
  26. Hexadecimal-to-Binary Conversion The conversion from Hexadecimal to binary is performed by converting each Hexadecimal digit to its 4-bit binary equivalent. This is illustrated below: 9F216 - 9 F 2

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