Computer Science

1
Computer Science

• LESSON ON
• Number Base Subtraction and Simple Equations

2
Objective

• In this lesson youll 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!

3
Review Base Ten Subtraction

• In Base 10 subtraction, you use a very simple
  process.
• Look at this problem
• 48
• -37
• 11

4
Review Base Ten Subtraction

• 48
• -37
• 11
• Each column is subtracted to get an answer of
  11pretty easy, huh?

5
Subtraction, Base 10

• Now look at this problem
• 63
• -37
• In this problem, you need to borrow.

6
Subtraction, Base 10

• 513
• 63
• -37
• Borrowing means taking a value from the next
  column and adding it to the column you need.

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.

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.

9
Subtraction, Base 10

• 513
• 63
• -37
• 26
• Then you subtract the two columns with a result
  of 26.

10
Subtraction, Base 8

• Now lets try base eight
• 63
• -37
• Again, in this problem, you need to borrow.

11
Subtraction, Base 8

• 511
• 63
• -37
• Borrow from the 6, which becomes five, and add 8
  to the 3, making 11!

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.

13
Subtraction, Base 8

• 511
• 63
• -37
• 24
• Then you subtract the two columns with a result
  of 24, base 8.

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!

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.

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.

17
Subtraction, Base 16

• Heres another example in base 16
• D6
• -3B
• How is this one solved? Try it.

18
Subtraction, Base 16

• C22
• D6
• -3B
• We must borrow from D, which becomes C, then add
  16 to 6, which makes 22.

19
Subtraction, Base 16

• C22
• D6
• -3B
• 9B
• 22 minus B (11) is B.
• C minus 3 is 9.
• Answer is 9B

20
Subtraction, Base 2

• Now base 2
• 11
• - 1
• 10
• This one is easyanswer is 10

21
Subtraction, Base 2

• Another in base 2
• 02
• 110
• - 1
• Here we need to borrow from the twos place

22
Subtraction, Base 2

• 02
• 110
• - 1
• 101
• Subtract to get the answer.

23
Subtraction, Base 2

• Still another in base 2
• 02
• 110
• - 11
• 1
• Now borrow again

24
Subtraction, Base 2

• 2
• 100
• - 11
• 11
• Final answer is 11, base 2

25
Simple Equations

• Here an equation to solve (base 10)
• x 6 14

26
Simple Equations

• Solutionsubtract 6 from both sides
• x 6 14
• -6 -6
• x 8

27
Simple Equations

• Now do it in base 8
• x 6 14

28
Simple Equations

• Solutionsubtract 6 from both sides
• x 6 14
• -6 -6
• x ?

29
Simple Equations

• Answer is 6, base 8
• 12
• x 6 14
• -6 -6
• x 6

30
Simple Equations

• Heres an equation in base sixteen (remember, A
  and F are NOT variables, but base sixteen
  values)
• x 2A F3

31
Simple Equations

• Solution?
• x 2A F3

32
Simple Equations

• Subtract 2A from both sides
• E19
• x 2A F3
• - 2A -2A
• x C9

33
Exercises

• Now try these exercises
• 12 - 12
• 78 - 68
• F16 - A16
• 158 - 68
• 4916 - 2B16
• CC16 - AD16

34
Exercises

• 738 - 348
• 3E16 2F16
• 1012 - 102
• 11012 - 112
• 10102 - 1112
• 7168 - 3648
• 7768 3378

35
Exercises

• Now lets mix it up a bit!
• AE16 768 _________8
• 2348 110110112 _________16
• 101102 - F16 768 _________10
• 38 3910 - 1101012 _________16
• 11112 - F16 1510 _________16

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

37
ANSWERS (JUMBLED)