John Owen, Rockport Fulton HS1 Computer Science LESSON ON Number Base Subtraction and Simple...
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John Owen, Rockport Fulton HS 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 101Subtract to get the answer.
John Owen, Rockport Fulton HS 23
Subtraction, Base 2
Still another in base 2: 02 110 - 11 1Now borrow again…
John Owen, Rockport Fulton HS 24
Subtraction, Base 2
2 100 - 11 11Final 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 -6x = 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 -6x = ?
John Owen, Rockport Fulton HS 29
Simple Equations
Answer is 6, base 8 12x + 6 = 14 -6 -6x = 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: E19x + 2A = F3 - 2A -2Ax = C9
John Owen, Rockport Fulton HS 33
Exercises
Now try these exercises1. 12 - 12 =
2. 78 - 68 =
3. F16 - A16 =
4. 158 - 68 =
5. 4916 - 2B16 =
6. CC16 - AD16 =
John Owen, Rockport Fulton HS 34
Exercises
7. 738 - 348 =
8. 3E16 – 2F16 =
9. 1012 - 102 =
10. 11012 - 112 =
11. 10102 - 1112 =
12. 7168 - 3648 =
13. 7768 + 3378 =
John Owen, Rockport Fulton HS 35
Exercises
Now let’s mix it up a bit!14. AE16 + 768 = _________8
15. 2348 + 110110112 = _________16
16. 101102 - F16 + 768 = _________10
17. 38 + 3910 - 1101012 = _________16
18. 11112 - F16 + 1510 = _________16
John Owen, Rockport Fulton HS 36
Exercises
And finally, some equations19. x16 + 7616 = AB16
20. x2 - 10112 = 1012
21. x8 + 568 = 728
22. x2 + 2510 = 1F16
23. x8 + 3748 - 65568 = BAD16
24. 378 + X16 = 110111102
John Owen, Rockport Fulton HS 37
ANSWERS (JUMBLED)35
37
69
110
177
332
354
1010
0
1
5
7
11
11
14
19
1335
10000
14037
1E
1F
BF
F
F