If natural numbers are original things, then the method of recording these numbers is artificial. Man-made things must be varied, so the number system will be varied.
The ancient Babylonians used the hexadecimal system, and humans still used the hexadecimal system when recording time and angle. 60 is divisible by 2,3,4,5,6, 10, 12,15,20,30. It contains as many factors as 10, and among the numbers within 100, it has the most factors, only 90. But 96 is much bigger than 60. In this way, when dividing by 60, decimals can appear less. This is why hexadecimal is still in use today. But this number is relatively large, requiring 60 different symbols, which is more troublesome.
The British still adhere to the 12 system in weights and measures, such as one pound equals 12 ounce and one foot equals 12 inch. The English system has brought a lot of trouble to the world.
However, some people in the United States organized a 12 system association, and publicly stated that human beings should use 12 system instead of 10 system. Their reason is that 12 can be divisible by 2, 3, 4 and 6, and there are relatively few opportunities for decimals in division. However, 10 only has factors 2 and 5, so it is very troublesome to be divisible by the frequently occurring 3, 4 and 6. Although these claims of the United States are reasonable, they will certainly not work. Because habit has become nature.
The simplest number system is binary, in which there are only two numbers, 0 and 1. To represent two numbers, it must be written as10; Third, it should be written as11; Four will be written as100; Seven should be written as111; Eight will be written as four digits, 1000. It is troublesome to calculate binary with a pen. However, in the computer world, they all use binary because they only have two "fingers": the on and off of the circuit. Of course, computers use binary not only because the circuit has only two states, but also because it is the best in storage capacity and counting speed compared with other binary systems. In addition, binary has the simplest multiplication table and the simplest addition table, and the conversion between binary and decimal is very convenient, which are the advantages of binary.
10 and 12 use few symbols, and the number of bits required to record a number is not much, which conforms to two notation principles: 1. Use as few symbols as possible; 2。 Remember a number with as few numbers as possible. Hexadecimal recording of a number requires few digits, but too many symbols. Binary recording requires the least symbols, but it requires a long string of numbers. Fortunately, computers are not afraid of long strings of numbers.
It is said that the binary system was invented by the German mathematician Leibniz, and the specific time was about 1672- 1676. He said that he was inspired by China's gossip. 1679 In March, Leibniz wrote a paper entitled Binary Arithmetic. In this paper, binary numbers are discussed comprehensively and compared with decimal numbers, and the correct rules of addition and multiplication of binary numbers are given.