Unit 1
Math 116
Number
Systems
Unit One
Number Systems
Sections 1.1 - 1.2
Introduction to
Number Systems
Through out history civilizations have keep records using their own number systems.
This unit will introduce some basic number systems that were used by past civilizations.
Examples of Ancient
Number Systems
1) Egyptian
2) Attic
3) Roman
4) Mayan
5) Traditional Chinese
6) Babylonian
I)
Egyptian
Number System
The Egyptian use symbols to represent the values that are multiple of ten.
The symbols are written in figure 1-1
Figure 1.1
|
1 = |
|
staff |
|
10 = |
|
heel bone |
|
100 = |
|
coil of rope |
|
1000 = |
|
lotus flower |
|
10,000 = |
|
pointing finger |
|
100,000 = |
|
tadpole |
|
1,000,000 = |
|
astonished man |
(This chart is provided by the Department of Mathematics and
Statistics at
These symbols were provided by http://eyelid.ukonline.co.uk/ancient/numbers.htm
=Millions 
=Hundred
Thousands 
=Ten
Thousands
=Thousands
=Hundreds
=Tens
=Ones
Examples
Write the following numbers as an Egyptian number.
1) 345
(Symbols courtesy http://eyelid.ukonline.co.uk/ancient/numbers.htm)
2) 456
(Symbols courtesy http://eyelid.ukonline.co.uk/ancient/numbers.htm)
3) 45623
(Symbols courtesy http://eyelid.ukonline.co.uk/ancient/numbers.htm)
II)
Roman
Numerals
Roman Numerals are very similar to the Egyptian system, but are based on 5 instead of 10.
The Roman Numerals
|
Symbol |
Number Value |
|
I |
1 |
|
V |
5 |
|
X |
10 |
|
L |
50 |
|
C |
100 |
|
D |
500 |
|
M |
1000 |
|
|
5000 |
|
|
10000 |
|
|
50000 |
|
|
100000 |
|
|
500000 |
|
|
1000000 |
Examples
Convert the following decimal number to a Roman numeral.
1) 25
XXV
2) 246
200 = CC
40 = XL
6 = VI
So, the final answer would be
CCXLVI
3) 1989
1000 = M
900 = CM
80 = LXXX
9 = IX
Final Answer: MCMLXXXIX
4) 13020
5) 1148
M = 1000
C = 100
XC = 40
VIII = 8
Final answer
MCXCVIII
III)
The Mayan
System
The Mayan system came into existence about 300 BC. This system is based on 18 and 20. The Mayans were the first to use the concept
of zero. The number zero was denoted by the symbol 
Mayan symbols
|
Symbol |
Number Value |
|
|
0 |
|
• |
1 |
|
•• |
2 |
|
••• |
3 |
|
•••• |
4 |
|
|
5 |
|
|
6 |
|
|
7 |
|
|
8 |
|
|
9 |
|
|
10 |
|
|
11 |
|
|
12 |
|
|
13 |
|
|
14 |
|
|
15 |
Number Systems
Section 1.3
Binary numbers
Babylonians system was based on 60
The Mayan system was based on 20
Our number system is based on 10
Computer use a number system based on 2 (Binary)
|
System |
Base |
Digits |
Place Values |
|
Binary |
2 |
0,1 |
1,2,4,8,16,32 |
|
Quintary |
5 |
0,1,2,3,4 |
1,5,25,125,625 |
|
Octal |
8 |
0,1,2,3,4,5,6,7 |
1,8,64,512,4096 |
Binary numbers
Using binary numbers, you would count as follows:
0
1
10
11
100
101
110
111
1000
.
.
.
Converting a based
number other than base 10 to base 10
Write each of the following on a decimal numeral
1) Convert the base 2 (Binary) number to base 10
2) Convert the base 2 (Binary) number to base 10
3) Convert 243 to a base 2 number (Binary Number)
4) Convert 165 to a binary number
5) Convert 121 to a binary number
6) Convert 1112 to a base ten number
7) Convert 110112 to a base 10 number
Optional Notes
(Using numbers other than base two or base ten)
7) Convert 245 into a base 5
number. (Optional)
8) Convert 49 into a base 6
number. (Optional)
1)
Optional (Convert to base 10)
2) Optional (Convert to base 10)
