Sept 2, 2002
Name__________________________________
Course Number Math 1476
NUMBER SYSTEMS: Part II
Do you really know how our number system works?
Quick Review: Then New Stuff
Base 10: Decimal System
The ten symbols used in base 10 are 0-9
Each digit is holding a place. The place holder is multiplied by a power of 10.
The number 7419 is really...
741910 = 7 x 103 + 4 x 102
Base 2: Binary System
+ 1 x 101
+ 9 x 100
The two symbols used in base 2 are 0-1
Each digit is holding a place. The place holder is multiplied by a power of 2.
1101012 = 1 x 25 + 1 x 24 + 0 x 23
=
1101012 =
32 + 16
5310
Converting 65310 to Base 2:
2 |653
2 |326
2 |163
2 | 81
2 | 40
2 | 20
2 | 10
2| 5
2| 2
2| 1
2| 0
+
0
+ 1 x 22 + 0 x 21
+
4
+
0
+ 1 x 20
+
1
R1
R0
R1
R1
R0
R0
R0
R1
R0
R1
Ans: 10100011012
Verify the answer is correct.
10100011012 =
= 1 x 29 + 0 x 28 + 1 x 27 + 0 x 26 + 0 x 25 + 0 x 24 +1 x 23 + 1 x 22 + 0 x 21 + 1 x 20
= 512 + 0
+ 128 + 0
+ 0
+ 0
+ 8
+ 4
+ 0
+ 1
= 65310
Base 8: Octal System
5238
5238
The eight symbols used in base 8 are 0-7
Each digit is holding a place. The place holder is multiplied by a power of 8.
= 5 x 82
+ 2 x 81
= 320
+ 16
= 33910
+ 3 x 80
+
3
Converting 65310 to Base 8:
8 |653
8 |81
8 |10
8|1
|0
R5
R1
R2
R1
Ans: 12158
Verify the answer is correct.
12158 =
= 1 x 83 + 2 x 82 + 1 x 81 + 5 x 80
= 512 + 128 + 8
+ 5
= 65310
Practice Problems:
A) Convert the following base 10 numbers to base 8:
1) 75
2) 281
3) 471
B) Convert the following base 8 numbers to base 10:
1) 678
2) 10118
3) 1458
Answers:
A1: 1138
B1: 55
A2: 4318
B2: 521
A3: 7278
B2: 101
If you didn’t get the answers above, try to ask questions that will help you learn the procedure. There are no
stupid questions…
Things to be thinking about for next class:
How would you write numbers in base 16 (Hexadecimal)?
How many symbols would you need? What are they?
What procedure do you think might convert a base 10 number to a base 16 number?