Cse 112 number system-[id_142-15-3472]
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This document presents an overview of different number systems including decimal, binary, octal, and hexadecimal. It defines each system, their bases, and the digits used. Conversion methods between the systems are described, such as repeated division to convert decimal to binary and multiplying place values to convert in the opposite direction. The relationships between the different bases are shown, including that hexadecimal represents groups of 4 binary digits. Examples are provided for conversions between the various number systems.
Cse 112 number system-[id_142-15-3472]
- 2. Presented by Name : Md. Abu Noman Jumaed ID : 142-15-3472 Dept. : CSE Faculty : FSIT
- 3. 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
- 4. INTRODUCTION In early days when there were no means of counting, people use to count with the help of fingers, stones, sticks, etc. These methods were not adequate and had many limitations. Many number system were introduced with the passage of time like: Decimal Number System Binary Number System Octal Number System Hexadecimal Number System
- 5. 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 85,48,35,456 etc.
- 6. BINARY NUMBER SYSTEM • The Binary Number System consist of only two digits– 0 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.
- 7. Why Binary? Since the computer is made up of electronic components; it can have only two states, either • On(1) • 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.
- 8. 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.
- 9. 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.
- 10. Relationship between Hexadecimal, Octal, Decimal, and Binary 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. Hexadeci mal Octal Decimal Binary 0 0 0 0000 1 1 1 0001 2 2 2 0010 3 3 3 0011 4 4 4 0100 5 5 5 0101 6 6 6 0110 7 7 7 0111 8 10 8 1000 9 11 9 1001 A 12 10 1010 B 13 11 1011 C 14 12 1100 D 15 13 1101 E 16 14 1110 F 17 15 1111
- 12. Decimal-to-Binary Conversion The method of converting Decimal to binary is repeated-division method. For conversion follow the rules: 1. Divide the given decimal number with the base 2. 2. Write down the remainder and divide the quotient by 2. 3. Repeat step 2 till the quotient is zero.
- 13. Convert 20010 to Binary Number Reading the remainders from the bottom to top, the result is 20010 = 110010002 2 200 Remainders 2 100 0 LSB 2 50 0 2 25 0 Write 2 12 1 in 2 6 0 this 2 3 0 order 2 1 1 0 1 MSB
- 14. Binary-to-Decimal Conversion To convert a binary number follow the steps: 1. Multiply each binary number with 2 having the power 0 for last position, starting from the right digit. 2. Increase the power one by one, with base as 2. 3. Sum up all the products to get decimal number.
- 15. Convert 1100010012 to Decimal Number 1100010012= 1 X 28 + 1 𝑋 27 + 0 𝑋 26 + 0 𝑋 25 + 0 𝑋 24 + 1 𝑋 23 + 0 𝑋 22 + 0 𝑋 21 1 𝑋 20 = 256 + 128 + 0 + 0 + 0 + 8 + 0 + 0 + 1 = 393 Thus, 1100010012 = 39310
- 16. Decimal-to-Octal The method of converting Decimal to Octal is repeated-division method. For conversion follow the rules: 1. Divide the given decimal number with the base 8, 2. Write down the remainder and divide the quotient by 8, 3. Repeat step 2 till the quotient is zero.
- 17. Convert 50010 to Octal Number Reading the remainders from the bottom to top, the result is 26610 = 4128 8 266 Remainders 8 33 2 LSB 8 4 1 0 4 MSB
- 18. Octal-to-Decimal Conversion To convert a octal number follow the steps: 1. Multiply each Octal number with 8 having the power 0 for last position, starting from the right digit. 2. Increase the power one by one, with base as 8. 3. Sum up all the products to get decimal number.
- 19. Convert (372)8 to Decimal Number 3728 = 3 X 82 + 7 𝑋 81 + 2 𝑋 80 = 3 X 64 + 7 X 8 + 2 X 1 = 192 + 56 + 2 = 25010 Thus, 3728 = 25010 So, an octal number can be easily converted to its decimal equivalent by multiplying each octal digit by its position weight.
- 20. 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: Using these conversions, any octal number is converted to binary by individually converting each digit. Octal Digit 0 1 2 3 4 5 6 7 Binary Equivalent 000 001 010 011 100 101 110 111
- 21. Convert 54318 to Binary Number We convert 54318 to binary using 3 bits for each octal digit as follows: 5 4 3 1 101 100 011 001 Thus, 54318 = 1011000110012
- 22. 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 0s. 3. Each group Is converted to its octal equivalent. It illustrated below for binary number 11010110 0 1 1 0 1 0 1 1 0 3 2 6 Thus, 110101102 = 3268
- 23. Decimal-to-Hexadecimal Conversion The method of converting Decimal to Hexadecimal is repeated-division method. For conversion follow the rules: 1. Divide the given decimal number with the base 16. 2. Write down the remainder and divide the quotient by 16. 3. Repeat step 2 till the quotient is zero.
- 24. Convert 42310 to Hexadecimal Reading the remainders from the bottom to top, the result is 42310 = 1𝐴716 Note: Any remainder greater than 9 are represented by letters A through F. 16 423 Remainders 16 26 7 LSB 16 1 A 0 1 MSB
- 25. Hexadecimal-to-Decimal Conversion To convert a Hexadecimal number follow the steps: 1. Multiply each hexadecimal number with 16 having the power 0 for last position, starting from the right digit. 2. Increase the power one by one, with base as 16. 3. Sum up all the products to get decimal number.
- 26. Convert 2𝐴𝐹16 to Decimal Number 2𝐴𝐹16 = 2 X 162 + 10 𝑋 161 + 15 𝑋 160 = 512 + 160 + 15 = 68710 Thus, 2𝐴𝐹16 = 68710
- 27. 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 0s. 3. Each group Is converted to its Hexadecimal equivalent. It illustrated below for binary number 1010111010 0 0 1 0 1 0 1 1 1 0 1 0 2 B A Thus, 10101110102 = 2𝐵𝐴16
- 28. 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 1001 1111 0010 Thus, 9𝐹216 = 1001111100102
- 29. References Computer Fundamentals By Dr. M Lutfar Rahman & Dr. M Alamgir Hossain Computer Fundamentals By Pradeep K. Sinha & Priti Sinha http://www.byte-notes.com/number-system- computer
- 30. Thank You
- 31. Any Query???