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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

Computer Science

LESSON ON

Number Base Subtraction and Simple Equations

John Owen, Rockport Fulton HS

objective
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

review base ten subtraction
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

review base ten subtraction1
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

subtraction base 10
Subtraction, Base 10
  • Now look at this problem:

63

-37

  • In this problem, you need to borrow.

John Owen, Rockport Fulton HS

subtraction base 101
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

subtraction base 102
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

subtraction base 103
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

subtraction base 104
Subtraction, Base 10

513

63

-37

26

  • Then you subtract the two columns with a result of 26.

John Owen, Rockport Fulton HS

subtraction base 8
Subtraction, Base 8
  • Now let’s try base eight:

63

-37

  • Again, in this problem, you need to borrow.

John Owen, Rockport Fulton HS

subtraction base 81
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

subtraction base 82
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

subtraction base 83
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

subtraction base 16
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

subtraction base 161
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

subtraction base 162
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

subtraction base 163
Subtraction, Base 16

Here’s another example in base 16

D6

-3B

  • How is this one solved? Try it.

John Owen, Rockport Fulton HS

subtraction base 164
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

subtraction base 165
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

subtraction base 2
Subtraction, Base 2

Now base 2:

11

- 1

10

  • This one is easy…answer is 10

John Owen, Rockport Fulton HS

subtraction base 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

subtraction base 22
Subtraction, Base 2

02

110

- 1

101

Subtract to get the answer.

John Owen, Rockport Fulton HS

subtraction base 23
Subtraction, Base 2

Still another in base 2:

02

110

- 11

1

Now borrow again…

John Owen, Rockport Fulton HS

subtraction base 24
Subtraction, Base 2

2

100

- 11

11

Final answer is 11, base 2

John Owen, Rockport Fulton HS

simple equations
Simple Equations

Here an equation to solve (base 10):

x + 6 = 14

John Owen, Rockport Fulton HS

simple equations1
Simple Equations

Solution…subtract 6 from both sides

x + 6 = 14

-6 -6

x = 8

John Owen, Rockport Fulton HS

simple equations2
Simple Equations

Now do it in base 8:

x + 6 = 14

John Owen, Rockport Fulton HS

simple equations3
Simple Equations

Solution…subtract 6 from both sides

x + 6 = 14

-6 -6

x = ?

John Owen, Rockport Fulton HS

simple equations4
Simple Equations

Answer is 6, base 8

12

x + 6 = 14

-6 -6

x = 6

John Owen, Rockport Fulton HS

simple equations5
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

simple equations6
Simple Equations

Solution?

x + 2A = F3

John Owen, Rockport Fulton HS

simple equations7
Simple Equations

Subtract 2A from both sides:

E19

x + 2A = F3

- 2A-2A

x =C9

John Owen, Rockport Fulton HS

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

John Owen, Rockport Fulton HS

exercises1
Exercises
  • 738 - 348 =
  • 3E16 – 2F16 =
  • 1012 - 102 =
  • 11012 - 112 =
  • 10102 - 1112 =
  • 7168 - 3648 =
  • 7768 + 3378 =

John Owen, Rockport Fulton HS

exercises2
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

exercises3
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

answers jumbled
ANSWERS (JUMBLED)

John Owen, Rockport Fulton HS