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 24) + (1 x 23) (1 x 22) + (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
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