Interesting Math History 


Question : 
What is 'Binary System' of arithmetic ? 
Answer : 
Binary means consisting of two parts or things. The Binary number
system is actually a system of notation which uses the base
2 combined with place value of notation. Since the scale is
2, there are only two digits or bigits 0 and 1. If there is
one more than 1, we turn from the unit's place to the two's
place, thus 1 + 1 = 10 
To convert any number such as 31 (scale 10) to scale 2, repeated division by 2 is necessary.
31
÷ 2 
= 
15
R1 
15
÷ 2 
= 
7
R1 
7
÷ 2 
= 
3
R1 
3
÷ 2 
= 
1
R1 

Therefore 31 (Scale 10) = (1 x 2^{4}) + (1 x 2^{3}) (1 x 2^{2}) + (1 x 2) + (1 x 1) = 11,111
in scale 2. 
Base
10 
Binary
System 
1 
1 
2 
10 
3 
11 
4 
100 
5 
101 
6 
110 
7 
111 
8 
1000 
9 
1001 
10 
1010 
11 
1011 
12 
1100 
13 
1101 
14 
1110 
15 
1111 
16 
10000 
17 
10001 
18 
10010 
19 
10011 
20 
10100 

The binary system plays an important role in technology and computer science.
More importantly, the binary system underlies the modern technology of electronic digital computers. Computer memory
comprises small elements that may only be in two states  off/on  that are associated with digits 0 and 1. Such an
element is said to represent one bit  binary digit.
Conversion :
Convert decimal 50 to binary:
50/2 = 25 remainder 0
25/2 = 12 remainder 1
12/2 = 6 remainder 0
6/2 = 3 remainder 0
3/2 = 1 remainder 1
1/2 = 0 remainder 1
To known the binary number read the remainders from bottom to top. Answer is 110010.
Convert binary 11110 to decimal :
0 * 1 = 0
1 * 2 = 2
1 * 4 = 4
1 * 8 = 8
1 * 16= 16
Answer is 0 + 2 + 4 + 8 + 16 = 30

