Integer part, which converts decimal into binary until the quotient is 0. Read the remainder from bottom to top. The remainder is the integer part of a binary number. For the decimal part, multiply by 2 to get the result of its integer part, and then repeat the calculation with the calculated decimal part until the decimal part is all 0, and then read all the calculated integer parts from top to bottom.
Binary to octal:
It is also easy to convert binary into octal, because the radix of octal is 8, and 8 is the power of 2 (8 = 23), so one bit of octal needs exactly three binary bits to represent it. The correspondence between octal numbers and binary numbers is the first eight hexadecimal numbers in the above table. Binary number 000 is octal number 0, binary number11is octal number 7, and so on.
Precautions:
Generally speaking, numbers come from the accumulation and calculation of objects, and natural numbers are produced one after another. Today, the most commonly used counting method in the world is decimal, which has become an indispensable part of people's lives.
Decimalization was invented by ancient Indians. From 2500 BC to 65438 BC+0750 BC, the ancient Indians adopted the decimal counting method. First, they invented the nine number symbols 1-9 and the positioning counting method, and then put forward the theory of zero-sum decimal as the basic point of calculus.
The reason why Indians follow the rule of "one in ten" is probably because they use 10 fingers to assist in counting. In decimal system, the only odd numbers to be counted are 0, 1, 2, 39. Many ethnic groups in Central Asia have gradually adopted this simple counting method.
Later, the Arabs conquered India, revised India's 10 number and spread it to Europe. Indian numerals and their calculation methods have gradually evolved into the Arabic counting method widely used in the world today.
China also has a long history in studying and using counting methods. Judging from the pottery pieces unearthed in archaeology, as early as five or six thousand years ago in primitive society, our ancestors had mastered natural numbers within 30.
In the middle of Shang Dynasty, there were 13 numbers in pottery tablets and Oracle Bone Inscriptions: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 100, 1,000 and 10,000 respectively.
In the long-term social practice, people find that adjacent numbers in different positions are very easy to be confused, so they create a vertical and horizontal calculation method. From the 8th century BC to the 3rd century BC, that is, during the Spring and Autumn Period and the Warring States Period, strict decimal system appeared in China. This is the great creation of China's ancient mathematics. Until the middle of15th century, abacus became the main calculation tool.
Refer to the above content: Baidu Encyclopedia-Decimal System