PDT DC015 Chapter 2 Computer System 2017/2018 (d)
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The document discusses number systems including binary, decimal, and hexadecimal. It provides examples of converting between these number systems. Key points covered include: - Binary uses 0 and 1, decimal uses 0-9, and hexadecimal uses 0-9 and A-F - Conversions can be done between any two number systems by placing the value in the appropriate column based on the system's base (e.g. binary is base 2, decimal is base 10, hexadecimal is base 16) - Examples are provided for converting decimal to binary, binary to decimal, decimal to hexadecimal, hexadecimal to decimal, and between binary and hexadecimal.
![UPS 2015/2016
Q: Given the Internet Protocol address of a
printer as 192.0.0.2. Convert the address to
hexadecimal number [2 marks]
A: C0.0.0.2](https://image.slidesharecdn.com/cpdtchapter022-170704055943/85/PDT-DC015-Chapter-2-Computer-System-2017-2018-d-42-320.jpg)
PDT DC015 Chapter 2 Computer System 2017/2018 (d)
- 1. 1 NUMBER SYSTEM AND REPRESENTATION 2.2 Number System 2.2.1 Binary 2.2.2 Hexadecimal 2.2.3 Conversion Between Binary and Hexadecimal Chapter PDT - 2017/2018
- 2. Define Number System ● A set of numerals for representing numbers Decimal Numbers (base 10) Binary Numbers (base 2) Hexadecimal Numbers (base 16) Page 260 Figure 5-2 8 Discovering Computers : Chapter 5
- 3. Decimal Numbers ● Consists of numbers 0-9 ● Decimal digits are joined together to form longer decimal numbers ● Example: 1, 2, 3, 4, 5, 6, 7, 8, 9,10, 11, 12,……… ● also known as the base 10 numbering system 8 6 1 5 6 x 10^2 1 x 10^1 5 x 10^0 6 x 100 1 x 10 5 x 1 600 + 10 + 5 = 615
- 4. At the end of this topic, students should be able to: represent data in binary forma) 1 NUMBER SYSTEM AND REPRESENTATION 2.2.1 Binary Chapter PDT - 2017/2018
- 5. Binary Numbers ● Machine recognises two states: 0 (off) and 1 (on) ● Binary number represents numeric values using two symbols, 0 and 1 ● Eg : 111000, 101 111 111 8
- 6. Comparison Between Decimal Number and Binary Number 8 DECIMAL BINARY 0 0 1 1 2 10 3 11 4 100 5 101 6 110 DECIMAL BINARY 7 111 8 1 000 9 1 001 10 1 010 11 1 011 . . 40 101 000 . .
- 7. At the end of this topic, students should be able to: represent data in hexadecimal forma) 1 NUMBER SYSTEM AND REPRESENTATION 2.2.2 Hexadecimal Chapter PDT - 2017/2018
- 8. Hexadecimal Numbers ● Uses 16 symbols: 0,1,2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E and F. ● It can represent binary values in compact form. ● 9B416 is example of hexadecimal numbers. 8
- 9. Comparison Between Decimal Number and Hexadecimal Number 8 DECIMAL HEXADECIMAL 0 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 DECIMAL HEXADECIMAL 10 A 11 B 12 C 13 D 14 E 15 F 16 10 17 11 20 14 35 23
- 10. 8 Decimal Hexadecimal Binary 0 0 0 1 1 1 2 2 10 3 3 11 4 4 100 5 5 101 6 6 110 7 7 111 8 8 1000 9 9 1001 10 A 1010 11 B 1011 12 C 1100 13 D 1101 14 E 1110 15 F 1111 Comparison Between Number System
- 11. At the end of this topic, students should be able to: a. convert from binary to hexadecimal b. convert from hexadecimal to binary 1 NUMBER SYSTEM AND REPRESENTATION 2.2.3 Conversion Between Binary and Hexadecimal Chapter PDT - 2017/2018
- 12. Conversion Between Number System ● Decimal to Binary ● Binary to Decimal ● Decimal to Hexadecimal ● Hexadecimal to Decimal ● Binary to Hexadecimal ● Hexadecimal to Binary 8
- 13. CONVERSION Decimal to Binary conversion
- 14. Binary number 2 2 ---- 0 ---- 1 2 2 ---- 1 ---- 0 22 11 5 2 1 0 ---- 1 Hence, 22 = 10110 2 Eg 1: Convert the number 22 to the binary number system. Solution : 22 = 2 2 Write from bottom to top → left to right Decimal to binary conversion
- 15. Eg 2: Convert the number 40 to the binarynumber system. Solution : 40 = 2 2 2 2 2 2 2 40 20 10 5 2 1 0 ---- 0 ---- 0 ---- 0 ---- 1 ---- 0 ---- 1 Binary number Hence, 40 = 101000 2 Write from bottom to top → left to right Decimal to binary conversion
- 16. 2 2 2 2 2 18 9 4 2 1 0 ---- 0 ---- 1 ---- 0 ---- 0 ---- 1 Binary number Hence, 18 = 100102 Eg 3:Express 18 in binary number form Solution 18 = 2 Write from bottom to top → left to right Decimal to binary conversion
- 17. CONVERSION Binary to Decimal conversion
- 18. ● In binary number, the column weights (again from right to left) are as follows: ● Eg : convert 1011 2 to decimal number Binary to Decimal conversion 1 0 1 1 1 x (2^3) 0 x (2^2) 1 x (2^1) 1 x (2^0) 1 x 8 0 x 4 1 x 2 1 x 1 Decimal number 8 0 2 1 8+0+2+1=1110 Binary to decimal conversion CONVERSION Eg 1: Convert the number 10112 to the decimal
- 19. Hence, 10110 2 = 22 Eg 1: Convert the binary number 10110 2 to decimal number Solution: 1 0 1 1 0 1 x 2^4 0 x 2^3 1 x 2^2 1 x 2^1 0 x 2^0 2210 1 x 16 0 x 8 1 x 4 1 x 2 0 x 1 16 0 4 2 0 16 + 0 + 4 + 2 + 0 = Binary to decimal conversion CONVERSION Eg 2: Convert the number 101102 to the decimal
- 20. Eg 2 :Convert the binary number 1011100 2 to decimal number Solution: Hence, 1 011 100 2 = 92 1 0 1 1 1 0 0 1 x 2^6 0 x 2^5 1 x 2^4 1 x 2^3 1 x 2^2 0 x 2^1 0 x 2^0 9210 1 0 1 1 1 0 0 1 x 64 0 x 32 1 x 16 1 x 8 1 x 4 0 x 2 0 x 1 64 + 0 + 16 + 8 + 4 + 0 + 0 = Binary to decimal conversion CONVERSION Eg 3: Convert the number 10111002 to the decimal
- 22. 16 16 16 1341 83 5 0 ---- 3 ---- 5 Eg 1: Convert the decimal number 1341 to hexadecimal number Hence,1341 = 53D16 Decimal to hex conversion Hex Number Write from bottom to top → left to right ---- 13 = D
- 23. Eg 2 : Convert the decimal number 860 to hexadecimal number 16 16 16 860 53 3 0 ---- 12 = C ---- 5 ---- 3 Hence, 860 = 35C16 Hex Number Decimal to hex conversion Write from bottom to top → left to right
- 24. 16 16 16 2020 126 7 0 ---- 4 ---- 14 = E ---- 7 Eg 3 : Convert the decimal number 2020 to hexadecimal number Hex Number Decimal to hex conversion Hence, 2020 = 7E416 Write from bottom to top → left to right
- 26. to decimal number● Convert AFB216 Solution: Hence, AFB216 = 44978 Eg 1 : Convert the hex number, AFB216 to decimal number A F B 2 A x 16^3 F x 16^2 B x 16^1 2 x 16^0 4497810 10 x 4096 15 x 256 11 x 16 2 x 1 40960 + 3840 + 176 + 2 = hex to decimal conversion CONVERSION Eg 1: Convert the number AFB16 to the decimal
- 27. to decimal number● Convert BA816 Solution: Hence, BA816 = 2984 Eg 2 : Convert the hex number, BA816 to decimal number B A 8 B x 6^2 A x 16^1 8 x16^0 298410 11 x 256 10 x 16 8 x 1 2816 + 160 + 8 = hex to decimal conversion CONVERSION Eg 2: Convert the number BA816 to the decimal
- 28. to decimal number● Convert AFFA16 Solution: Hence, AFFA16 = 45050 Eg 3 : Convert the hex number, AFFA16 to decimal number A F F A A x 16^3 F x 16^2 F x 16^1 A x16^0 4505010 10 x 4096 15 x 256 15 x16 10 x 1 40960 + 3840 + 240 + 10 = hex to decimal conversion CONVERSION Eg 3: Convert the number AFFA16 to the decimal
- 30. Binary to Hexadecimal conversion ● There are two ways on how to convert the binary to hexadecimal number. ● 1st way : Decimal Hexadecimal ○ Binary ○ 2nd way : ○ Binary Hexadecimal binary to hex conversion
- 31. Eg. 1: Convert the binary number 110102 to hexadecimal 1st way ○ Binary Decimal 26 1 16 16 0 ---- 10 = A ---- 1 Decimal Hexadecimal Hence, 11010 2 = 1A16 1 1 0 1 0 1 x 2^4 1 x 2^3 0 x 2^2 1 x 2^1 0 x 2^0 26 1 x16 1 x8 0 x 4 1 x 2 0 x 1 16 + 8 + 0 + 2 + 0 = Eg. 1: Convert the binary number 110102 to hexadecimal 1st way
- 32. ● Step 1: divide the given binary digit into 4 digit per group from right to left. 1 1 0 1 0 ● Step 2: Using 8421 table, 1 1 0 1 0 1 = 1 8 4 2 1 8 + 2 = 10 = A 8 4 2 1 Hence, 11010 2 = 1A16 Eg. 1: Convert the binary number 110102 to hexadecimal 2nd way
- 33. Binary Decimal binary to hex conversion 18 1 0 ---- 2 ---- 1 Decimal 16 16 Hexadecimal Hence, 100102 = 1216 Hex number Eg.2 :Convert the binary number 100102 to hexadecimal 1st way 1 0 0 1 0 1 x 2^4 0 x 2^3 0 x 2^2 1 x 2^1 0 x 2^0 18 1 x 16 0 x 8 0 x 4 0 x 2 0 x 1 16 + 0 + 0 + 2 + 0 = Eg. 2: Convert the binary number 100102 to hexadecimal 1st way
- 34. Eg.2 :Convert the binary number 100102 to hexadecimal 2nd way ● Step 1: divide the given binary digit into 4 digit per group from right to left. 1 0 0 1 0 ● Step 2: Using 8421 table, 1 0 0 1 0 1 = 1 8 4 2 1 2 = 2 8 4 2 1 Hence, 11010 2 = 1216
- 36. Hexadecimal to Binary conversion ● There are two ways on how to convert the hexadecimal to binary number. ● 1st way : Decimal Binary ○ Hexadecimal ○ 2nd way : ○ Hexadecimal Binary binary to hex conversion
- 37. Eg 1: Convert the hexadecimal number 3FD to binary number 1st way Hexadecimal Decimal 16^2 16^1 16^0 1021 3 F D 256 x3 16 x15 1 x 13 768 + 240 + 13 = hex to binary conversion Eg. 1: Convert the hexadecimal number 3FD16 to binary number 1st way Hexadecimal Decimal
- 38. Binary number De 2 2 2 2 1021 510 ---- 1 255 ---- 0 127 ---- 1 2 63 ---- 1 2 31 ---- 1 2 15 ---- 1 2 7 ---- 1 2 3 ---- 1 2 1 ---- 1 Hence, 3FD16 = 11111111012 0 ---- 1 cimal Binary hex to binary conversion Eg. 1: Convert the hexadecimal number 3FD16 to binary number 1st way
- 39. Eg 1: Convert the hexadecimal number 3FD to binary number 2nd way Hence, 3FD16 = 11111111012 =8+4+1 = 13 =8+4+2+1 = 15 =2+1 = 3 3 F = 15 D = 13 3 15 13 8 4 2 1 8 4 2 1 8 4 2 1 0 0 1 1 1 1 1 1 1 1 0 1 Eg. 1: Convert the hexadecimal number 3FD16 to binary number 2nd way hex to binary conversion
- 40. Eg 2: Convert the hexadecimal number 1A2 to binary number 1st way hex to binary conversion Hexadecimal Decimal Decimal Binary 2 2 2 2 2 2 2 2 2 2 ---- 0 ---- 1 ---- 0 ---- 0 ---- 0 ---- 1 ---- 0 ---- 1 ---- 1 Hence, 1A216 = 1101000102 1 A 2 1 x 16^2 A x 16^1 2 x 16^0 418 1 x 256 10 x 16 2 x 1 256 + 160 + 2 = 418 209 104 52 26 13 6 3 1 0 Eg. 2: Convert the hexadecimal number 1A216 to binary number 1st way DecimalHexadecimal Decimal Binary hex to binary conversion
- 41. Eg 2: Convert the hexadecimal number 1A2 to binary number 2nd way =2=8+2 = 10 =1 Hence, 1A216 = 1101000102 1 A 2 1 10 2 8 4 2 1 8 4 2 1 8 4 2 1 0 0 0 1 1 0 1 0 0 0 1 0 = 2= 8 + 2 = 10 = 1 Eg. 2: Convert the hexadecimal number 1A216 to binary number 2nd way hex to binary conversion
- 42. UPS 2015/2016 Q: Given the Internet Protocol address of a printer as 192.0.0.2. Convert the address to hexadecimal number [2 marks] A: C0.0.0.2