Interesting Math History

Question :
What is 'Binary System' of arithmetic ?

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 LINKS DISCLAIMER CONTACT US