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State Board of Technical Education & Training Andhra Pradesh

e – Lesson Module for C-16 Curriculum. State Board of Technical Education & Training Andhra Pradesh. Year/Semester : III Semester Branch : Electronics and Communication Engg Subject : EC-303, Digital Electronics Topic : Basics of digital electronics

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State Board of Technical Education & Training Andhra Pradesh

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  1. e – Lesson Module for C-16 Curriculum State Board of Technical Education & Training Andhra Pradesh Year/Semester : III Semester Branch : Electronics and Communication Engg Subject : EC-303, Digital Electronics Topic : Basics of digital electronics Sub Topic :Octal to binary conversion &vice-versa :Hexadecimal to Binary conversion &vice- versa Duration : 50 min Prepared by T.MadhaviKumari,Lecturer in ECE Under the guidance of G.V.V.S.Murty, Head of ECE Government Polytechnic for Women , Kakinada C-16-EC-303-1.4

  2. Objectives On completion of this period, you will be able to Convert a Octal number to Binary number & Vice-versa. Covert a Hexadecimal to Binary conversion &vice-versa Convert a Octal number to Hexadecimal number & vice versa C-16-EC-303-1.4

  3. Octal to Binary conversion Octal Digit 3 bit binary • Replace each octal digit by its 3-bit binary equivalent • The eight octal digits and 3 bit binary equivalent 0 000 1 001 2 010 3 011 4 100 5 101 6 110 Click here:O- B conversion video 7 111 C-16-EC-303-1.4

  4. Octal to binary conversion • For example : Convert octal 1736 into binary Octal digits --- 1 7 3 6 • 3- bit binary • equivalent • 110 001 111 • 011 (1736)8 =(1111011110)2 C-16-EC-303-1.4

  5. Octal to binary conversion • Convert octal 45.1 into binary Octal digits --- 4 5 . 1 • 3- bit binary • equivalent 100 101 . 001 Ans: (45.1)8 = (100101.001)2 C-16-EC-303-1.4

  6. Binary to Octal Conversion The binary number is converted into groups of 3 bits each, starting at binary point. Make groups of 3 bits starting from binary point & moving towards left for Integer part Make groups of 3 bits starting from binary point & moving towards right for fractional part Add 0’s to the left of integer and right of the fractional part whenever necessary Replace each group of three bits by its Octal digit Click here:B- O conversion video C-16-EC-303-1.4

  7. Binary to Octal Conversion (Contd) • For Example: convert (1001111.11)2 to its octal. • The given number is grouped into 3-bits as 1 001 111 . 11 • By adding zero’s on left side and right side the same is written a 001 001 111 . 110 1 1 7 . 6 (1001111.11)2 = (117.6)8 C-16-EC-303-1.4

  8. Example: Convert (0.10100110)2 to its equivalent octal number (0.10100110)2 = (0.101 001 100)2 0.5 1 4 Binary to Octal Conversion (Contd..) (0.10100110)2 = (0.514)8 C-16-EC-303-1.4

  9. Hexadecimal to binary conversion • To convert a hexadecimal number to a binary number, • convert each hexadecimal digit to its 4-bit equivalent binary. 9 Hexa decimal Digit 4 bit binary Hexa decimal Digit 4 bit binary 0 0000 8 1000 1 0001 9 1001 2 0010 A 1010 3 0011 B 1011 4 0100 C 1100 5 0101 D 1101 6 0110 E 1110 7 0111 F 1111 Click here: H- B conversion video C-16-EC-303-1.4

  10. Hexadecimal to Binary conversion • For example : 9AF . 3 Hexadecimal is Converted to Binary as follows: Hex digits --- 9 A F . 3 • 4- bit binary • equivalent . • 0011 1001 1010 • 1111 (9AF.3)16 =(100110101111.0011)2 C-16-EC-303-1.4

  11. Binary to Hexadecimal Conversion The binary number is converted into groups of 4 bits each, starting at binary point. Make groups of 4 bits starting from binary point & moving towards left for Integer part Make groups of 4 bits starting from binary point & moving towards right for fractional part Add 0’s to the left of integer and right of the fractional part whenever necessary Replace each group of 4 bits by its Hexadecimal digit Click here: B- H conversion video C-16-EC-303-1.4

  12. Binary to Hexadecimal conversion • For example the binary number is 1011001001. • Group of 4-bits 10 1100 1001 • By adding zero’s on left side 0010 1100 1001 2 9 C 10110010012 = 2C916 C-16-EC-303-1.4

  13. Binary to Hexadecimal conversion • A given fractional binary number can be converted into hexadecimal number by grouping the given binary number into 4- bits. • For example the binary number is 0.1011001001. • The grouping should be considered from LSB towards MSB • in 4bits for integer parts. • 0.1011 0010 01 • By adding zero’s on right side • 0. 1011 0010 0100 • 0. B 2 4 C-16-EC-303-1.4

  14. Octal to Hexadeciamal Conversion • To convert octal to hexadecimal • First convert Octal to Binary • Convert the resultant binary to hexadecimal Click here:O-B-H conversion video C-16-EC-303-1.4

  15. Hexadecimal to Octal Conversion • To convert hexadecimal to octal • First convert hexadecimal to Binary • Convert the resultant binary to octal Click here:H-B-O conversion video C-16-EC-303-1.4

  16. C-16-EC-303-1.4

  17. C-16-EC-303-1.4

  18. C-16-EC-303-1.4

  19. Binary Decimal Repeatedly divide by 2 Octal Decimal Repeatedly divide by 8 Hexadecimal Decimal Repeatedly divide by 16 C-16-EC-303-1.4

  20. Video Lectures Click here:O- B conversion video Click here:B- O conversion video Click here: H- B conversion video Click here: B- H conversion video Click here:O-B-H conversion video Click here:H-B-O conversion video C-16-EC-303-1.4

  21. Binary Decimal multiply with Positional weights Power of 2 Octal Decimal multiply with Positional weights Power of 8 Hexa decimal Decimal multiply with Positional weights Power of 16 C-16-EC-303-1.4

  22. Summary Octal Groups of 3 bits Binary Hexa decimal Binary Groups of 4 bits C-16-EC-303-1.4

  23. Assignments • Convert the following octal numbers into binary • 246.478 • 561.028 • 732.678 • Convert the following binary numbers into octal • 1101.1012 • 1111011.112 • 1011.10112 C-16-EC-303-1.4

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