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4589327 0101010 ABFC...

4589327 0101010 ABFC. Objectives Upon completion of this chapter, 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. Perform binary and hexadecimal arithmetic. Number systems.

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4589327 0101010 ABFC...

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  1. 4589327 0101010 ABFC...

  2. Objectives Upon completion of this chapter, 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. • Perform binary and hexadecimal arithmetic. Number systems

  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. E.g. 3 4 5 Introduction

  4. 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. E.g. 3 4 5 Introduction Click TO Continue

  5. 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. E.g. 3 4 5 100>> 1s position 101>> 10s position 102>> 100s position Introduction

  6. 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. Beside decimal number, binary (Base 2), octal (Base 8), and hexadecimal (Base 16) are commonly used in the digital electronics system.

  7. 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. Beside decimal number, binary (Base 2), octal (Base 8), and hexadecimal (Base 16) are commonly used in the digital electronics system.

  8. Under construction Under construction Ready Ready Ready Binary Octal Hexadecimal Number Arithmetic Other commonly used number systems Tutorial Tutorial

  9. In digital electronics, we only deal with 2 voltage levels (High or Low; On or OFF), for this reason, almost all digital systems (base 2) use the binary number system as the system of its operations. Binary number system

  10. 1 0 4 8 20 21 22 23 Binary number are strings of two (hence ‘bi’) symbols 0’s, that represent numbers. They may be expanded in the usual way with a base of 2. E.g. 11012 + 1310 Binary number system Click TO Continue

  11. 110112 = (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 Whole number Convert 111012 todecimal number Binary – to – decimal conversion Click TO Continue

  12. 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 Try the following Convert 101102 todecimal number Click TO Continue

  13. 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 Fraction number Convert 101.1012 todecimal number Binary – to – decimal conversion Click TO Continue

  14. Solution 110.112 = (1)*22 + (1)*21 + (0)*20 + (1)*2-1 + (1)*2-2 = 4 + 2 + 0 + 0.5 + 0.25 = 6.7510 Try the following Convert 110.112 todecimal number Click TO Continue

  15. 2 510 Remainder 25 2 = 1 1 0 01 2 12 12 1 0 LSB 2 6 0 1 2 3 2 1 1 2 0 MSB Whole number Convert 2510 todecimal number by repeated division Decimal – to – binary conversion Click TO Continue

  16. Solution Remainder 30 2 2 15 0 1 Ans 2 7 1 1 2 3 = 111102 2 1 1 2 0 Try the following Convert 3010 tobinary number Click TO Continue

  17. Carry 0.375 x 2 = 0.75 0.375 x 2 = 0.75 0 0.75 x 2 = 0.5 1 0.37510 0.5 x 2 = 0 1 = 0.011 Fraction number Convert 0.37510 todecimal number by repeated multiplication Decimal – to – binary conversion Click TO Continue

  18. Solution Whole number Fraction number Carry Remainder 15 2 2 7 1 1 0.125 x 2 = 0.25 0 Ans 2 3 0.25 x 2 = 0.5 0 1 1 2 1 = 1111.0012 0.5 x 2 = 0 1 2 0 Try the following Convert 15.12510 tobinary number Click TO Continue

  19. 101110102 2 7 2 Binary can easily converts 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 Convert 101110102 todecimal number Binary – to – Octal conversion Click TO Continue

  20. 111 101 0112 Solution 7 5 3 Try the following Convert 1111010112 todecimal number Click TO Continue

  21. 1 16 448 1536 80 81 82 83 Octal number are base 8 number. It uses symbols 0, 1, 2, 3, 4, 5, 6, 7. E.g. 37218 + 200110 Octal number system Click TO Continue

  22. 3268 = (3)*82 + (2)*81 + (6)*80 = 3*64 + 2*8 + 6*1 = 192 + 16 + 6 = 21410 Whole number Convert 3268 todecimal number Octal – to – decimal conversion Click TO Continue

  23. Solution 2778 = (2)*82 + (7)*81 + (7)*80 = 128 + 56 + 7 = 19110 Try the following Convert 2778 todecimal number Click TO Continue

  24. 33010 Remainder 330 8 = 5128 8 41 2 1 LSD 8 5 5 MSD 8 0 Convert 33010 todecimal number by repeated division Decimal – to – octal conversion Click TO Continue

  25. Solution Remainder 230 8 8 26 2 0 Ans 8 2 2 0 = 2028 Try the following Convert 23010 tooctal number Click TO Continue

  26. 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. E.g. 4AF216 + 1918610 Hexadecimal number system Click TO Continue

  27. 2FE16 = (2)*162 + (F)*161 + (E)*160 = 2*256 + 15*16 + 14*1 = 512 + 240 + 14 = 76610 Whole number Convert 2FE16 todecimal number Hexadecimal – to – decimal conversion Click TO Continue

  28. Solution 2A616 = (2)*162 + (10)*161 + (6)*160 = 512 + 160 + 6 = 67810 Try the following Convert 2A616 todecimal number Click TO Continue

  29. 49810 Remainder 498 16 = 1F216 16 31 2 F LSD 16 1 1 MSD 16 0 Convert 49810 todecimal number by repeated division Decimal – to – Hexadecimal conversion Click TO Continue

  30. Solution Remainder 255 16 16 15 F F Ans 16 0 = FF16 Try the following Convert 25510 tooctal number Click TO Continue

  31. 1011 1010 10102 B A A Binary can easily converts into Hexadecimal symbol by forming the binary number into group of 4 bits, and each group is then directly into a Hexadecimal number. Convert 1011101010102 tohexadecimal number Binary – to – Hexadecimal conversion Click TO Continue

  32. 1000 1111 00112 Solution 8 F 3 Try the following Convert 1111010112 todecimal number Click TO Continue

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