Transcript Number Base Arithmetic Lesson 2
Discrete Math LESSON ON Number Base Subtraction and Simple Equations 1
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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Review Base Ten Subtraction In Base 10 subtraction, you use a very simple process.
Look at this problem: 48 -37 = 11 3
Review Base Ten Subtraction 48 -37 = 11 Each column is subtracted to get an answer of 11…pretty easy, huh?
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Subtraction, Base 10 Now look at this problem: 63 -37 In this problem, you need to borrow.
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Subtraction, Base 10 5 13 63 -37 Borrowing means taking a value from the next column and adding it to the column you need.
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Subtraction, Base 10 5 13 63 -37 In this case, borrow from the 6, which becomes five, and add 10 to the 3, making 13.
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Subtraction, Base 10 5 13 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.
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Subtraction, Base 10 5 13 63 -37 26 Then you subtract the two columns with a result of 26.
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Subtraction, Base 8 Now let’s try base eight: 63 -37 Again, in this problem, you need to borrow.
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Subtraction, Base 8 5 11 63 -37 Borrow from the 6, which becomes five, and add 8 to the 3, making 11!
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Subtraction, Base 8 5 11 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.
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Subtraction, Base 8 5 11 63 -37 24 Then you subtract the two columns with a result of 24, base 8.
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Subtraction, Base 16 Now base 16: 5 19 63 -37 Again, we borrow from the 6, which becomes five, and add 16 to the 3, making 19!
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Subtraction, Base 16 5 19 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.
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Subtraction, Base 16 5 19 63 -37 2C In the ones column, 19 minus 7 is 12 , which is C in base sixteen, with 2 in the second column.
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Subtraction, Base 16 Here’s another example in base 16 D6 -3B How is this one solved? Try it.
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Subtraction, Base 16 C 22 D6 -3B We must borrow from D, which becomes C, then add 16 to 6, which makes 22.
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Subtraction, Base 16 C 22 D6 -3B 9B 22 minus B (11) is B.
C minus 3 is 9.
Answer is 9B 19
Subtraction, Base 2 Now base 2: 11 - 1 10 This one is easy…answer is 10 20
Subtraction, Base 2 Another in base 2: 0 2 110 1 Here we need to borrow from the twos place… 21
Subtraction, Base 2 0 2 110 1 101 Subtract to get the answer.
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Subtraction, Base 2 Still another in base 2: 0 2 110 - 11 1 Now borrow again… 23
Subtraction, Base 2 2 1 0 0 - 11 11 Final answer is 11, base 2 24
Simple Equations Here an equation to solve (base 10): x + 6 = 14 25
Simple Equations Solution…subtract 6 from both sides x + 6 = 14 -6 -6 x = 8 26
Simple Equations Now do it in base 8: x + 6 = 14 27
Simple Equations Solution…subtract 6 from both sides x + 6 = 14 -6 -6 x = ?
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Simple Equations Answer is 6, base 8 12 x + 6 = 14 -6 -6 x = 6 29
Simple Equations Here’s an equation in base sixteen (remember, A and F are NOT variables, but base sixteen values): x + 2A = F3 30
Simple Equations Solution?
x + 2A = F3 31
Simple Equations Subtract 2A from both sides: E 19 x + 2A = F3 - 2A -2A x = C9 32
Exercises 1.
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Now try these exercises 1 2 - 1 2 = 7 8 F 16 - 6 8 - A = 16 = 15 8 49 16 - 6 8 - 2B = 16 CC 16 - AD 16 = = 33
Exercises 7.
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73 8 3E 16 - 34 8 – 2F = 16 = 101 2 1101 2 - 10 2 - 11 2 = = 1010 2 716 8 - 111 - 364 8 2 = = 776 8 + 337 8 = 34
Exercises Now let’s mix it up a bit!
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AE 16 + 76 8 = _________ 8 234 8 + 11011011 2 10110 2 - F 16 + 76 8 = _________ 16 = _________ 10 3 8 + 39 10 - 110101 2 1111 2 - F 16 + 15 10 = _________ = _________ 16 16 35
Exercises And finally, some equations 19.
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x 16 + 76 16 = AB 16 x 2 x 8 - 1011 2 = 101 2 + 56 8 = 72 8 x x 2 8 37 8 + 25 10 = 1F 16 + 374 + X 16 8 - 6556 8 = BAD 16 = 11011110 2 36
0 1 5 7 11 11 14 19 ANSWERS (JUMBLED) 35 37 69 110 177 332 354 1010 1335 10000 14037 1E 1F BF F F 37