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Number Systems

Number Systems . Different number systems Representation of numbers in binary Conversion between decimal and binary, Conversion between binary and hexadecimal Use of subscripts 2, 10 and 16 for bases. Number Systems . Decimal number system – Base 10 = 1, 2 ,3 4, 5, ect ..

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Number Systems

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  1. Number Systems Different number systems Representation of numbers in binary Conversion between decimal and binary, Conversion between binary and hexadecimal Use of subscripts 2, 10 and 16 for bases

  2. Number Systems • Decimal number system – Base 10 = 1, 2 ,3 4, 5, ect.. • Binary number system –Base 2 = 0001, 0010, 0011, ect… • Hexadecimal number system = Base 16 = 9, A, B, 4C ect…

  3. Decimal Number Systems • Decimal numbers are base 10 • They are made up of 10 numbers – 0,1,2,3,4,5,6,7,8,9. • Combining the ten numbers will create units, tens, hundreds and thousands

  4. Split the following decimal numbers

  5. Answers

  6. Binary Number System • Binary numbers are base 2 • Computer language • They are made up of 2 numbers – 1 and 0

  7. Hexadecimal Number Systems • Hexadecimal numbers are base 16 • Computer memory locations • They are made up of 16 numbers

  8. Importance of Base numbers • Writing the base numbers is very important as; • 1510 and 1516 are not the same number but without the base they would be both considered as the same number • 1010 and 102 are not the same number as 102 represents 210

  9. Complete the table

  10. Answers

  11. Converting Binary to Decimal

  12. Explanation • Write down the placement value on top of each number. • Write the values that are on (the ones with a one under them • Add the numbers together

  13. Example • We want to convert 110012 to decimal

  14. Working • Convert the following to decimal • 1010102 • 1110112 • 101010012 • 0011001112 • 1110101002

  15. Answers • Convert the following to decimal • 1010102 = 4210 • 1110112 =5910 • 101010012 =16910 • 0011001112 =10310 • 1110101002 =46810

  16. Converting Decimal to Binary

  17. Method One • Write down the placement values of binary • Chose the numbers that add up to you decimal number • Put a 1 under the numbers used to add up to your decimal number

  18. Example • Convert 4610 to binary

  19. Method Two • Divide the original number by 2 and write down the remainder even if it is 0 • Keep on dividing the decimal numbers by 2 until 1 is divided by 2 • Write down the remainders next to each other starting from the bottom moving upwards

  20. Example • Convert 4610 to binary Ans 4610 = 1011102

  21. Working • Convert the following decimal numbers to binary • 1010 • 6610 • 12010 • 3510 • 8810

  22. Answers • Convert the following decimal numbers to binary • 1010 = 10102 • 6610 =10000102 • 12010 =11110002 • 3510 =1000112 • 8810 =10110002

  23. Converting Binary to Hexadecimal

  24. Explanation • Split the binary number into groups of 4 1001110 = 0100 – 1110 • Write the 2x on top of each number starting from the right • Add the numbers that are on • Write down thetotals, if a total is larger than 9, convert it to the hex letter NOTE: when we do not have enough bits lefts to create a group of 4 we add 0s

  25. Example • Convert 11001112 in Hexadecinal

  26. Working • Convert the following into Hexadecimal • 1110101002 • 11101112 • 1010102 • 1112 • 11100012

  27. Working • Convert the following into Hexadecimal • 1110101002 = 1D416 • 11101112 = 7716 • 1010102 = 2A16 • 1112 = 716 • 11100012 = 7116

  28. Converting Hexadecimal to Binary

  29. Explanation • Write each individual number in the hexadecimal number eg B416 • Write the binary placement values for each hex number • List 1s under the placement values that are on • 4.Write the split binary number as one whole number

  30. Example • Convert 2C16 to binary

  31. Working • Convert the following hex numbers to binary • AB16 • F716 • 1516 • CC16 • 2216

  32. Answers • Convert the following hex numbers to binary • AB16 = 101010112 • F716 = 111101112 • 1516 = 000101012 • CC16 = 110011002 • 2216 = 001000102

  33. Converting Decimal to Hexadecimal

  34. Method One • Divide the decimal number by 16 taking note of the remainders • Keep on dividing the whole number by 16 until the whole number obtained is 0. • Write down the remainders next to each other starting from the bottom, changing numbers greater than 9 to letters ANS = 1D116

  35. Example • Convert 80010 to hexadecimal ANS = 32016

  36. Method Two • Convert the decimal number to binary • Convert the binary number to hexadecimal Eg, changing 45610 to hexadecimal

  37. Example • Convert 80010 to hexadecimal

  38. Working • Convert the following to Hexadecimal numbers • 34010 • 11910 • 6610 • 2510 • 11110

  39. Answers • Convert the following to Hexadecimal numbers • 34010 = 15416 • 11910 =7716 • 6610 =4216 • 2510 =1916 • 11110 =6F16

  40. Converting Hexadecimal to Decimal

  41. Explanation • Writing down the placement values on top of each number starting with 160 • Multiply the top value with the hexadecimal number. • Add all the results Converting 43A16 to decimal

  42. Working • Convert the following into decimal • 5516 • CB16 • F816 • B416 • 9016

  43. Answers • Convert the following into decimal • 5516 = 8510 • B016 =17610 • 2F816 =76010 • B416=18010 • 9016 =14410

  44. Homework • Copy and complete this table

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