john owen, rockport fulton hs1 computer science lesson on number base addition
TRANSCRIPT
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John Owen, Rockport Fulton HS 1
Computer Science
LESSON ON Number Base
Addition
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John Owen, Rockport Fulton HS 2
Objective
In this lesson you’ll learn how to do simple addition in Base 2, 8, and 16.
It is essentially the same as Base 10 addition, just in a different base!
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John Owen, Rockport Fulton HS 3
Review Base Ten Addition, #1
In Base 10 addition, you learned a very simple process.
Look at this problem: 12
+37 First add the ones column,
then the tens.
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John Owen, Rockport Fulton HS 4
Review Base Ten Addition, #1
12
+37
49
The answer is 49…simple, right?
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John Owen, Rockport Fulton HS 5
Review Base Ten Addition, #2
Now look at this problem: 13 +37 When you add the ones
column values, the result of 10 EQUALS the base value of 10, so you have to CARRY a 1.
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John Owen, Rockport Fulton HS 6
Review Base Ten Addition, #2
1 13 +37 0 When a carry is made, you essentially
divide by 10 (the base) to determine what value to carry, and mod by 10 to determine what value to leave behind.
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John Owen, Rockport Fulton HS 7
Review Base Ten Addition,#2
1 13 +37 0 3 plus 7 is 10 10 divided by 10 is 1 (carry) 10 mod 10 is 0 (leave)
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John Owen, Rockport Fulton HS 8
Review Base Ten Addition, #2
1 13 +37 50
Answer is 50
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John Owen, Rockport Fulton HS 9
Review Base Ten Addition, #3
Here’s a third example: 16 +37 When you add the ones
column values, the result of 13 EXCEEDS the base value of 10, so CARRY a 1.
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John Owen, Rockport Fulton HS 10
Review Base Ten Addition, #3
16 +37 6 plus 7 is 13 13 divided by 10 is 1 (carry) 13 mod 10 is 3 (leave)
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John Owen, Rockport Fulton HS 11
Review Base Ten Addition, #3
1 16 +37 53 Answer is 53
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John Owen, Rockport Fulton HS 12
Review Base Ten Addition, #4
And finally, a fourth example: 76 +35 The ones column result of 11
EXCEEDS the base value of 10, and you CARRY a 1.
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John Owen, Rockport Fulton HS 13
Review Base Ten Addition,#4
1 76 +35 1 6 plus 5 is 11 11 divided by 10 is 1 (carry) 11 mod 10 is 1 (leave)
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John Owen, Rockport Fulton HS 14
Review Base Ten Addition, #4
1 76 +35 1 1+7+3 is 6 plus 5, which equals
11 11 divided by 10 is 1 (carry) 11 mod 10 is 1 (leave)
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John Owen, Rockport Fulton HS 15
Review Base Ten Addition, #4
1 76 +35 111 Answer is 111, base 10
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John Owen, Rockport Fulton HS 16
Base Eight Addition, #1
Now here is an example in base eight:
12 +34 When you add the ones column
values, the answer is 6, and the second column answer is 4.
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John Owen, Rockport Fulton HS 17
Base Eight Addition. #1
12 +34 46 Answer is 46, base eight You say, “four six base eight”, not
“forty-six” The phrase “forty-six” is meant for
base ten only.
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John Owen, Rockport Fulton HS 18
Base Eight Addition, #2
Now look at this problem: 14 +34 When you add the ones
column values, the result of 8 EQUALS the base value of 8, and you have to CARRY a one.
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John Owen, Rockport Fulton HS 19
Base Eight Addition, #2
14 +34 Again you divide by 8 (the base)
to determine what value to carry, and mod by 8 to determine what value to leave behind.
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John Owen, Rockport Fulton HS 20
Base Eight Addition, #2
1 14 +34 0 4 plus 4 is 8 8 divided by 8 is 1 (carry) 8 mod 8 is 0 (leave)
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John Owen, Rockport Fulton HS 21
Base Eight Addition, #2
1 14 +34 50 Answer is “five zero, base
eight”! Looks strange, but it is correct!
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John Owen, Rockport Fulton HS 22
Base Eight Addition, #3
Here’s a third example: 16 +37 When you add the ones
column values, the result of 13 EXCEEDS the base value of 8, and you have to CARRY a one.
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John Owen, Rockport Fulton HS 23
Base Eight Addition, #3
1 16 +37 5 6 plus 7 is 13 13 divided by 8 is 1 (carry) 13 mod 8 is 5 (leave)
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John Owen, Rockport Fulton HS 24
Base Eight Addition, #3
1 16 +37 55 Answer is 55, base eight.
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John Owen, Rockport Fulton HS 25
Base Eight Addition, #4
And a fourth example: 76 +35 The ones column result of 11
EXCEEDS the base value of 8, …CARRY a one.
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John Owen, Rockport Fulton HS 26
Base Eight Addition, #4
1 76 +35 3 6 plus 5 is 11 11 divided by 8 is 1 (carry) 11 mod 8 is 3 (leave)
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John Owen, Rockport Fulton HS 27
Base Eight Addition, #4
1 76 +35 33 1+7+3 is 6 plus 5 is 11 11 divided by 8 is 1 (carry) 11 mod 8 is 3 (leave)
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John Owen, Rockport Fulton HS 28
Base Eight Addition, #4
1 76 +35 133Answer is 133, base 8
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John Owen, Rockport Fulton HS 29
Base Two Addition, #1
Base Two Addition is quite interesting, but also fairly simple.
Since the only counting digits in base two are the values 0 and 1, there are only a few situations you have to learn.
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John Owen, Rockport Fulton HS 30
Base Two Addition, #1
We’ll start simple: 1 +1 =10 (“one zero, base two”) This looks strange, but the
same process applies.
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John Owen, Rockport Fulton HS 31
Base Two Addition, #1
1 +1 = 10 Since 1 + 1 is 2, this EQUALS
the base value of 2, which means you carry the “div” answer and leave the “mod” answer
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John Owen, Rockport Fulton HS 32
Base Two Addition, #1
1 +1 = 10 2 / 2 = 1 (carry) 2 % 2 = 0 (leave) That’s it!
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John Owen, Rockport Fulton HS 33
Base Two Addition, #2
Here’s another: 10 +11 = 101 Can you figure it out?
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John Owen, Rockport Fulton HS 34
Base Two Addition, #2
10 +11 = 101 In the ones column, 1 + 0 is 1. In the second column, 1+1 is
2, or 10 in base 2
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John Owen, Rockport Fulton HS 35
Base Two Addition, #3
And another: 101101 +110011
= Can you figure it out?
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John Owen, Rockport Fulton HS 36
Base Two Addition, #3
Step by step… 1 101101 +110011 = 0
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John Owen, Rockport Fulton HS 37
Base Two Addition, #3
Step by step… 1 101101 +110011 = 00
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John Owen, Rockport Fulton HS 38
Base Two Addition, #3
Step by step… 1 101101 +110011 = 000
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John Owen, Rockport Fulton HS 39
Base Two Addition, #3
Step by step… 1 101101 +110011 = 0000
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John Owen, Rockport Fulton HS 40
Base Two Addition, #3
Step by step… 1 101101 +110011 = 00000 Since 1+1+1 is 3, carry 1 and
leave 1
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John Owen, Rockport Fulton HS 41
Base Two Addition, #3
Step by step… 1 101101 +110011 =1100000 All done!
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John Owen, Rockport Fulton HS 42
Base Sixteen, Example #1
In base sixteen, remember the digits are 0-9, then A-F, representing the values 0-15
Here’s an example: 29 +12
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John Owen, Rockport Fulton HS 43
Base Sixteen, Example #1
29 +12 = 3B, base 16 2 + 9 is 11, which is B in base
sixteen 2+1 is 3, so the answer is 3B
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John Owen, Rockport Fulton HS 44
Base Sixteen, Example #2
1 A9 +47 = F0, base 16 9+7 is 16, equal to the base,
so carry 1 and leave 0 1 + A(10) + 4 is 15, which is F
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John Owen, Rockport Fulton HS 45
Base Sixteen, Example #3
11 D6 +7C = 152, base 16 6+C(12) = 18, carry 1, leave 2 1+D(13)+7 = 21, carry 1, leave
5
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John Owen, Rockport Fulton HS 46
Base Sixteen, Example #4
11 EF +2D = 11C, base 16 F(15) + D(13) = 28, carry 1, leave
C(12) 1 + E(14) + 2 = 17, carry 1, leave 1
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John Owen, Rockport Fulton HS 47
Exercises
Now try these exercises1. 12 + 12 =
2. 78 + 68 =
3. F16 + F16 =
4. 58 + 58 =
5. 916 + B16 =
6. C16 + D16 =
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John Owen, Rockport Fulton HS 48
Exercises
7. 38 + 48 =
8. F16 + 216 =
9. 102 + 102 =
10. 12 + 10112 =
11. 102 + 1102 =
12. 2168 + 3648 =
13. 7778 + 38 =
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John Owen, Rockport Fulton HS 49
Exercises
14. ACE16 + BAD16 =
15. 23416 + 97516 =
16. 4216 + F16 + 87616 =
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John Owen, Rockport Fulton HS 50
ANSWERS (JUMBLED)
7 11 12 10 14 15 19
1E 100 602 BA9 8C71000
1002 1100 167B