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Computer Science

Computer Science. LESSON ON Number Base Subtraction and Simple Equations. Objective. In this lesson you’ll learn how to do subtraction and how to solve simple equations involving Base 2, 8, and 16. Again, it is essentially the same concept as Base 10, just in a different base!.

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Computer Science

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  1. Computer Science LESSON ON Number Base Subtraction and Simple Equations John Owen, Rockport Fulton HS

  2. Objective • In this lesson you’ll learn how to do subtraction and how to solve simple equations involving Base 2, 8, and 16. • Again, it is essentially the same concept as Base 10, just in a different base! John Owen, Rockport Fulton HS

  3. Review Base Ten Subtraction • In Base 10 subtraction, you use a very simple process. • Look at this problem: 48 -37 = 11 John Owen, Rockport Fulton HS

  4. Review Base Ten Subtraction 48 -37 = 11 • Each column is subtracted to get an answer of 11…pretty easy, huh? John Owen, Rockport Fulton HS

  5. Subtraction, Base 10 • Now look at this problem: 63 -37 • In this problem, you need to borrow. John Owen, Rockport Fulton HS

  6. Subtraction, Base 10 513 63 -37 • Borrowing means taking a value from the next column and adding it to the column you need. John Owen, Rockport Fulton HS

  7. Subtraction, Base 10 513 63 -37 • In this case, borrow from the 6, which becomes five, and add 10 to the 3, making 13. John Owen, Rockport Fulton HS

  8. Subtraction, Base 10 513 63 -37 • When you borrow 1 from one column, it becomes the value of the base in the next column, or 10 in this case. John Owen, Rockport Fulton HS

  9. Subtraction, Base 10 513 63 -37 26 • Then you subtract the two columns with a result of 26. John Owen, Rockport Fulton HS

  10. Subtraction, Base 8 • Now let’s try base eight: 63 -37 • Again, in this problem, you need to borrow. John Owen, Rockport Fulton HS

  11. Subtraction, Base 8 511 63 -37 • Borrow from the 6, which becomes five, and add 8 to the 3, making 11! John Owen, Rockport Fulton HS

  12. Subtraction, Base 8 511 63 -37 • When you borrow 1 from a column, it becomes the value of the base in the next column, or 8 in this case. John Owen, Rockport Fulton HS

  13. Subtraction, Base 8 511 63 -37 24 • Then you subtract the two columns with a result of 24, base 8. John Owen, Rockport Fulton HS

  14. Subtraction, Base 16 Now base 16: 519 63 -37 • Again, we borrow from the 6, which becomes five, and add 16 to the 3, making 19! John Owen, Rockport Fulton HS

  15. Subtraction, Base 16 519 63 -37 • When you borrow 1 from a column, it becomes the value of the base in the next column, or 16 in this case. John Owen, Rockport Fulton HS

  16. Subtraction, Base 16 519 63 -37 2C • In the ones column, 19 minus 7 is 12, which is C in base sixteen, with 2 in the second column. John Owen, Rockport Fulton HS

  17. Subtraction, Base 16 Here’s another example in base 16 D6 -3B • How is this one solved? Try it. John Owen, Rockport Fulton HS

  18. Subtraction, Base 16 C22 D6 -3B • We must borrow from D, which becomes C, then add 16 to 6, which makes 22. John Owen, Rockport Fulton HS

  19. Subtraction, Base 16 C22 D6 -3B 9B • 22 minus B (11) is B. • C minus 3 is 9. • Answer is 9B John Owen, Rockport Fulton HS

  20. Subtraction, Base 2 Now base 2: 11 - 1 10 • This one is easy…answer is 10 John Owen, Rockport Fulton HS

  21. Subtraction, Base 2 Another in base 2: 02 110 - 1 • Here we need to borrow from the twos place… John Owen, Rockport Fulton HS

  22. Subtraction, Base 2 02 110 - 1 101 Subtract to get the answer. John Owen, Rockport Fulton HS

  23. Subtraction, Base 2 Still another in base 2: 02 110 - 11 1 Now borrow again… John Owen, Rockport Fulton HS

  24. Subtraction, Base 2 2 100 - 11 11 Final answer is 11, base 2 John Owen, Rockport Fulton HS

  25. Simple Equations Here an equation to solve (base 10): x + 6 = 14 John Owen, Rockport Fulton HS

  26. Simple Equations Solution…subtract 6 from both sides x + 6 = 14 -6 -6 x = 8 John Owen, Rockport Fulton HS

  27. Simple Equations Now do it in base 8: x + 6 = 14 John Owen, Rockport Fulton HS

  28. Simple Equations Solution…subtract 6 from both sides x + 6 = 14 -6 -6 x = ? John Owen, Rockport Fulton HS

  29. Simple Equations Answer is 6, base 8 12 x + 6 = 14 -6 -6 x = 6 John Owen, Rockport Fulton HS

  30. Simple Equations Here’s an equation in base sixteen (remember, A and F are NOT variables, but base sixteen values): x + 2A = F3 John Owen, Rockport Fulton HS

  31. Simple Equations Solution? x + 2A = F3 John Owen, Rockport Fulton HS

  32. Simple Equations Subtract 2A from both sides: E19 x + 2A = F3 - 2A-2A x =C9 John Owen, Rockport Fulton HS

  33. Exercises • Now try these exercises • 12 - 12 = • 78 - 68 = • F16 - A16 = • 158 - 68 = • 4916 - 2B16 = • CC16 - AD16 = John Owen, Rockport Fulton HS

  34. Exercises • 738 - 348 = • 3E16 – 2F16 = • 1012 - 102 = • 11012 - 112 = • 10102 - 1112 = • 7168 - 3648 = • 7768 + 3378 = John Owen, Rockport Fulton HS

  35. Exercises Now let’s mix it up a bit! • AE16 + 768 = _________8 • 2348 + 110110112 = _________16 • 101102 - F16 + 768 = _________10 • 38 + 3910 - 1101012 = _________16 • 11112 - F16 + 1510 = _________16 John Owen, Rockport Fulton HS

  36. Exercises And finally, some equations • x16 + 7616 = AB16 • x2 - 10112 = 1012 • x8 + 568 = 728 • x2 + 2510 = 1F16 • x8 + 3748 - 65568 = BAD16 • 378 + X16 = 110111102 John Owen, Rockport Fulton HS

  37. ANSWERS (JUMBLED) John Owen, Rockport Fulton HS

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