Decimal System  Binary System 
Base ten system  Base two system 
0,1,2,3,4,5,6,7,8,9  0,1 
Example: 234 that is (234)_{2} =
10^{2}  10^{1}  1^{0} 
2  3  4 
2x10^{2}  3x10^{1}  4x10^{0} 
200  30  4 
The number is 234

Example: 101 that is (101)_{2} =
2^{2}  2^{1}  2^{0} 
1  0  1 
1x2^{2}  0x2^{1}  1x2^{0} 
4x1  2x0  1x1 
The number is 4+1 = 5

Binary System:
Two digits "0" and "1" are used for computation in computers. This system is called Binary System (or the basetwo system) as the base digits are only two.
Table: Place value chart for Binary System
1 
1  Unit's Place 
2 
2  Two's Place 
2^{2} 
4  Four's Place 
2^{3} 
8  Eight's Place 
2^{4} 
16  Sixteen's Place 
2^{5} 
32  Thirty two's Place 
2^{6} 
64  Sixty Four's Place 
2^{7} 
128  One Hundred Twenty Eight's Place 
Method:
 Divide the number by 2. If it is divisible by 2, write 0. If not write 1.
 Take the quotient
 Divide the quotient by 2. If it is divisible by 2, write 0. If not write 1.
 Take the quotient and divide by 2
 Continue this process, until the number which we are left to divide by is 0.
Example:
Change (56)_{10} Into (______)_{2}.
2  56 
2  28  0  Unit's Place 
2  14  0  Two's Place 
2  7  0  Four's Place 
2  3  1  Eight's Place 
2  1  1  Sixteen's Place 
2  0  1  Thirty Two's Place 
The answer is third column from down to up, that is 111000 base two that is (111000)_{2}. This is read as oneoneonezerozerozero base two.
Directions: Change the Base Ten Numerals into Base Two Numerals. Also write at least 10 examples of your own.
