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4589327 0101010 ABFC...

Home page. Objectives. Introduction. Binary number system. Octal number system. 4589327 0101010 ABFC. Hexadecimal number system. Binary coded decimal. Click Next to continue. Objectives Upon completion of this Topic, you will be able to :

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4589327 0101010 ABFC...

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  1. Home page Objectives Introduction Binary number system Octal number system 4589327 0101010 ABFC... Hexadecimal number system Binary coded decimal Click Next to continue

  2. Objectives Upon completion of this Topic, you will be able to : • Differentiate the 4 commonly used number systems. • Convert numbers from one system to another. • Express decimal numbers using BCD code. Number systems Home page Objectives Introduction Binary number system Octal number system Hexadecimal number system Binary coded decimal Click Next to continue

  3. The decimal number system is familiar to everyone. This system uses the symbols 0,1,2,3,4,5,6,7,8,9. The decimal system is a positional system where each digit carries a certain weight based on its position. Introduction Home page Objectives Introduction Binary number system Octal number system Hexadecimal number system Binary coded decimal Click TO Continue

  4. E.g. 3 4 5 100>> 1s position 101>> 10s position 102>> 100s position The decimal number system is familiar to everyone. This system uses the symbols 0,1,2,3,4,5,6,7,8,9. The decimal system is a positional system where each digit carries a certain weight based on its position. Introduction Home page Objectives Introduction Binary number system Octal number system Hexadecimal number system Binary coded decimal Click Next to continue

  5. The decimal number system is also known as the base 10 system. It is referred to as base 10 because it has 10 different symbols. The base 10 system is also said to have radix of 10. Radix and base are terms that means exactly the same thing. Home page Objectives Introduction Binary number system e.g : 10110 Octal number system Hexadecimal number system Beside decimal number; binary (base 2), octal (base 8), and Hexadecimal (base 16) are commonly used in the digital electronics system. Binary coded decimal e.g : 1012 e.g : 1018 e.g : 10116 Click to evaluate the decimal value

  6. 5 10 64 10 257 10 The decimal number system is also known as the base 10 system. It is referred to as base 10 because it has 10 different symbols. The base 10 system is also said to have radix of 10. Radix and base are terms that means exactly the same thing. Home page Objectives Introduction Binary number system e.g : 10110 Octal number system Hexadecimal number system Beside decimal number; binary (base 2), octal (base 8), and Hexadecimal (base 16) are commonly used in the digital electronics system. Binary coded decimal e.g : 1012 e.g : 1018 e.g : 10116 Click on underlined words on the left to select lesson to learn…

  7. Objectives Upon completion of this lesson, you will be able to: Home page Objectives Introduction Binary number system Octal number system 1. Explain why the binary number system is ideal for digital logic applications. Hexadecimal number system Binary coded decimal 2. Convert decimal whole numbers and fractional numbers into binary numbers and vice versa. 3. Explain the following terms:- Bit, Nibble, Byte, and Word. Binary number system Click Next to continue

  8. 0 Low OFF  Open Home page Objectives Introduction In digital electronics, we only deal with 2 possible states (High and Low, On and OFF, or Open and Closed), for this reason, almost all digital systems use the binary (base 2) number system as the system of its operations. The two states of the binary number are:- 0 Binary number system Octal number system Hexadecimal number system Binary coded decimal Binary number system Click Next to continue

  9. 1 HighON Closed Home page Objectives Introduction In digital electronics, we only deal with 2 possible states (High and Low, On and OFF, or Open and Closed), for this reason, almost all digital systems use the binary (base 2) number system as the system of its operations. The two states of the binary number are:- 0 and 1 Binary number system Octal number system Hexadecimal number system Binary coded decimal Binary number system Click Next to continue

  10. 20 21 22 23 Binary number are strings of two (hence ‘bi’), symbols 0’s and 1’s, that represent numbers. They may be expanded in the usual way with a base of 2. Home page Objectives Introduction Binary number system Octal number system Hexadecimal number system E.g. 11012 Binary coded decimal Binary number system Click TO Continue

  11. 1 0 4 8 20 21 22 23 Binary number are strings of two (hence ‘bi’), symbols 0’s and 1’s, that represent numbers. They may be expanded in the usual way with a base of 2. Home page Objectives Introduction Binary number system Octal number system Hexadecimal number system E.g. 11012 Binary coded decimal + 1310 Binary number system Click Next to continue

  12. Home page Objectives Introduction Terminology Binary number system • Each digit in the binary number system is called a bit. • A group of four bits binary number is known nibble. • A group of eight bits binary number is known as byte. • Two bytes number form a word. Octal number system Hexadecimal number system Binary coded decimal Binary number system There are also terms for multiple bits using the standard range of prefixes, eg. , and . megabit (Mb) kilobit (Kb) gigabit (Gb) Click Next to continue

  13. Binary – to – decimal conversion Home page Objectives Introduction Whole number Binary number system Convert 111012 todecimal number Octal number system Hexadecimal number system Binary coded decimal Click TO Continue

  14. 111012 = (1)*24 + (1)*23 + (1)*22 + (0)*21 + (1)*20 = 1*16 + 1*8 + 1*4 + 0*2 + 1*1 = 16 + 8 + 4 + 0 +1 = 2910 Binary – to – decimal conversion Home page Objectives Introduction Whole number Binary number system Convert 111012 todecimal number Octal number system Hexadecimal number system Binary coded decimal Click Next to continue

  15. Home page Objectives Try the following Introduction Binary number system Convert 101102 todecimal number Octal number system Hexadecimal number system Binary coded decimal Click For Solution

  16. Solution 101102 = (1)*24 + (0)*23 + (1)*22 + (1)*21 + (0)*20 = 1*16 + 0*8 + 1*4 + 1*2 + 0*1 = 16 + 0 + 4 + 2 + 0 = 2210 Home page Objectives Try the following Introduction Binary number system Convert 101102 todecimal number Octal number system Hexadecimal number system Binary coded decimal Click Next to continue

  17. Binary – to – decimal conversion Home page Objectives Introduction Fraction number Binary number system Convert 101.1012 todecimal number Octal number system Hexadecimal number system Binary coded decimal Click TO Continue

  18. 101.1012 = (1)*22 + (0)*21 + (1)*20 + (1)*2-1 + (0)*2-2 + (1)*2-3 = 1*4 + 0*2 + 1*2 + 1*0.5 + 0*0.25 +1*0.125 = 4 + 0 + 1 + 0.5 + 0 + 0.125 = 5.62510 Binary – to – decimal conversion Home page Objectives Introduction Fraction number Binary number system Convert 101.1012 todecimal number Octal number system Hexadecimal number system Binary coded decimal Click Next to continue

  19. Home page Objectives Try the following Introduction Binary number system Convert 110.112 todecimal number Octal number system Hexadecimal number system Binary coded decimal Click For Solution

  20. Solution 110.112 = (1)*22 + (1)*21 + (0)*20 + (1)*2-1 + (1)*2-2 = 4 + 2 + 0 + 0.5 + 0.25 = 6.7510 Home page Objectives Try the following Introduction Binary number system Convert 110.112 todecimal number Octal number system Hexadecimal number system Binary coded decimal Click Next to continue

  21. Remainder 1 LSB 25 2 0 12 12 2 0 2 6 2 3 1 MSB 2 1 1 2 0 Decimal – to – binary conversion Home page Objectives Introduction Whole number Binary number system Convert 2510 todecimal number by repeated division Octal number system Hexadecimal number system Binary coded decimal Click TO Continue

  22. 2 510 Remainder 1 LSB 25 2 = 1 1 0 012 0 12 12 2 0 2 6 2 3 1 MSB 2 1 1 2 0 Decimal – to – binary conversion Home page Objectives Introduction Whole number Binary number system Convert 2510 todecimal number by repeated division Octal number system Hexadecimal number system Binary coded decimal Click Next to continue

  23. Solution 30 0 2 Remainder 15 1 2 Ans 1 2 7 2 3 1 = 111102 2 1 1 2 0 Home page Objectives Try the following Introduction Convert 3010 tobinary number Binary number system Octal number system Hexadecimal number system Binary coded decimal Click For Solution Click Next to continue

  24. Carry 0.375 x 2 = 0.75 0 0.75 x 2 = 0.5 1 0.37510 0.5 x 2 = 0 1 = 0.0112 Decimal – to – binary conversion Home page Objectives Introduction Fraction number Binary number system Convert 0.37510 todecimal number by repeated multiplication Octal number system Hexadecimal number system Binary coded decimal Click TO Continue Click Next to continue

  25. Whole number Fraction number Solution 13 Carry 2 Remainder 1 0.125 x 2 = 0.25 0 6 0 2 Ans 0 0.25 x 2 = 0.5 1 2 3 = 1101.0012 0.5 x 2 = 0 1 1 2 1 2 0 Home page Objectives Try the following Introduction Convert 13.12510 tobinary number Binary number system Octal number system Hexadecimal number system Binary coded decimal Click For Solution Click Next to continue

  26. Summary Upon completion of this lesson, you should to answer the following questions : • What is the weight of the 1s in the binary number 000 ? • What is the binary equivalent of decimal number ? • What is the decimal equivalent of binary number ? Home page Objectives Introduction Binary number system Octal number system 1 1 Hexadecimal number system Binary coded decimal 37 101.01 http://courses.cs.vt.edu/~cs1104/Bingo/bingo.kevin.html Click Next to continue

  27. Octal number system Home page • Objectives Upon completion of this lesson, you will be able to : • Convert decimal whole numbers into octal numbers and vice versa. • Convert binary numbers into octal numbers and vice versa. Objectives Introduction Binary number system Octal number system Hexadecimal number system Binary coded decimal Click Next to continue

  28. Home page Objectives Introduction Binary number system Octal number system Hexadecimal number system Binary coded decimal Octal number are base 8 number. It uses symbols 0, 1, 2, 3, 4, 5, 6, 7. Octal number system E.g. 37218 Click TO Continue

  29. Home page Objectives Introduction Binary number system Octal number system Hexadecimal number system Binary coded decimal 1 80 81 16 82 448 1536 83 + Octal number are base 8 number. It uses symbols 0, 1, 2, 3, 4, 5, 6, 7. Octal number system E.g. 37218 200110 Click Next to continue

  30. Octal – to – decimal conversion Home page Objectives Introduction Whole number Binary number system Convert 3268 todecimal number Octal number system Hexadecimal number system Binary coded decimal Click TO Continue

  31. 3268 = (3)*82 + (2)*81 + (6)*80 = 3*64 + 2*8 + 6*1 = 192 + 16 + 6 = 21410 Octal – to – decimal conversion Home page Objectives Introduction Whole number Binary number system Convert 3268 todecimal number Octal number system Hexadecimal number system Binary coded decimal Click Next to continue

  32. Home page Objectives Try the following Introduction Binary number system Convert 2778 todecimal number Octal number system Hexadecimal number system Binary coded decimal Click For Solution

  33. Solution 2778 = (2)*82 + (7)*81 + (7)*80 = 128 + 56 + 7 = 19110 Home page Objectives Try the following Introduction Binary number system Convert 2778 todecimal number Octal number system Hexadecimal number system Binary coded decimal Click Next to continue

  34. 330 8 Remainder 2 1 LSD 41 8 5 MSD 8 5 8 0 Decimal – to – octal conversion Home page Objectives Introduction Binary number system Convert 33010 todecimal number by repeated division Octal number system Hexadecimal number system Binary coded decimal Click TO Continue

  35. 330 33010 8 Remainder 2 1 LSD = 5128 41 8 5 MSD 8 5 8 0 Decimal – to – octal conversion Home page Objectives Introduction Binary number system Convert 33010 todecimal number by repeated division Octal number system Hexadecimal number system Binary coded decimal Click Next to continue

  36. Home page Objectives Try the following Introduction Convert 23010 tooctal number Binary number system Octal number system Hexadecimal number system Binary coded decimal Click For Solution

  37. Solution 230 8 Remainder 6 4 28 8 3 Ans 8 3 0 = 3468 Home page Objectives Try the following Introduction Convert 23010 tooctal number Binary number system Octal number system Hexadecimal number system Binary coded decimal Click Next to continue

  38. Binary – to – Octal conversion Home page Objectives Introduction Binary number system Binary can easily be converted into other based that are powers of 2, and each group of n bits converts directly into a symbol for another representation base -- 2 n Octal number system Hexadecimal number system Convert 101110102 tooctal (base 8) number 8 = 2 3 || where n =3 Binary coded decimal Click TO Continue

  39. 10 111 0102 2 7 2 Binary – to – Octal conversion Home page Objectives Introduction Binary number system Binary can easily be converted into other based that are powers of 2, and each group of n bits converts directly into a symbol for another representation base -- 2 n Octal number system Hexadecimal number system Convert 101110102 tooctal (base 8) number 8 = 2 3 || where n =3 Binary coded decimal Click Next to continue

  40. Home page Objectives Try the following Introduction Binary number system Convert 1111010112 tooctal number Octal number system Hexadecimal number system Binary coded decimal Click For Solution

  41. 111 101 0112 Solution 7 5 3 Home page Objectives Try the following Introduction Binary number system Convert 1111010112 tooctal number Octal number system Hexadecimal number system Binary coded decimal Click Next to continue

  42. Home page • Summary Upon completion of this lesson, you should to answer the following questions : • What is the weight of the 3 in the octal number 2 70 ? • What is the octal equivalent of decimal number ? • What is the octal equivalent of binary number ? Objectives Introduction Binary number system Octal number system Hexadecimal number system 3 Binary coded decimal 17 10111 Click on underlined words on the left to select lesson to learn…

  43. Hexadecimal number system Home page Objectives Upon completion of this lesson, you will be able to : Objectives Introduction Binary number system Octal number system • Convert decimal whole numbers into hexadecimal numbers and vice versa. • 2. Convert binary numbers into hexadecimal numbers and vice versa. Hexadecimal number system Binary coded decimal Click Next to continue

  44. Hexadecimal number are base 16 number. It uses symbols 0, 1, 2, 3, 4, 5, 6, 7,8.9,A,B,C,D,E,F. Home page Objectives Introduction Binary number system Octal number system Hexadecimal number system The Hex digit A to F are equivalent to decimal values 10 to 15 Binary coded decimal Hexadecimal number system Click TO Continue

  45. A16 1010 B16 1110 C16 1210 D16 1310 E16 1410 F16 1510 Hexadecimal number are base 16 number. It uses symbols 0, 1, 2, 3, 4, 5, 6, 7,8.9,A,B,C,D,E,F. Home page Objectives Introduction Binary number system Octal number system Hexadecimal number system The Hex digit A to F are equivalent to decimal values 10 to 15 Binary coded decimal Hexadecimal number system Click Next to continue

  46. 160 161 162 163 Hexadecimal number are base 16 number. It uses symbols 0, 1, 2, 3, 4, 5, 6, 7,8.9,A,B,C,D,E,F. Home page Objectives Introduction Binary number system Octal number system Hexadecimal number system E.g. 4AF216 Binary coded decimal Hexadecimal number system Click TO Continue

  47. 160 2 240 2560 16384 161 162 163 Hexadecimal number are base 16 number. It uses symbols 0, 1, 2, 3, 4, 5, 6, 7,8.9,A,B,C,D,E,F. Home page Objectives Introduction Binary number system Octal number system Hexadecimal number system E.g. 4AF216 Binary coded decimal + Hexadecimal number system 1918610 Click Next to continue

  48. Home page Objectives Introduction Whole number Binary number system Convert 2FE16 todecimal number Octal number system Hexadecimal number system Binary coded decimal Hexadecimal – to – decimal conversion Click TO Continue

  49. 2FE16 = (2)*162 + (F)*161 + (E)*160 = 2*256 + 15*16 + 14*1 = 512 + 240 + 14 = 76610 Home page Objectives Introduction Whole number Binary number system Convert 2FE16 todecimal number Octal number system Hexadecimal number system Binary coded decimal Hexadecimal – to – decimal conversion Click Next to continue

  50. Home page Objectives Try the following Introduction Binary number system Convert 2A616 todecimal number Octal number system Hexadecimal number system Binary coded decimal Click For Solution

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