How decimal and binary numbers are interchanged

If it's a method, I can give you a natural language description of how the decimal integer part n can be converted to binary as follows:

1) Divide n by 2, record the remainder, and save n's commercial n.

2) If n is not zero, proceed to the first step, otherwise, write the remainder sequence of the record in reverse order.

For example: decimal 25n = 25

n=12n=6

n=3n=1so.

The number of binary is 0,1, and the base is 2, which is characterized by every two into one, for example, binary is decimal (1022) 1 2 3+0 2 2+1 2 1+1 2 0=11. Decimal to binary - divide by two to take the remainder, the remainders are arranged in reverse order, such as 11, and the remainder obtained by dividing by two in order is 011, and the remainder is 110 in reverse order. Pure handmade mobile phone typing, hey.

Divide by 2, the remainder continues to divide by 2, and the final remainder is arranged.

For example, 15, 15 divided by 2 equals 7 more (1). 7 divided by 2 equals 3 more (1). 3 divided by 2 equals 1 surplus (1). 1 divided by 2 equals 0 (1).

Then the binary representation of 15 is 1111

Another example is divided by 2 equals 8 more (0).

8 divided by 2 equals 4 surplus (0), 4 divided by 2 equals 2 surplus (0), 2 divided by 2 equals 1 surplus (0), 1 divided by 2 about 0 surplus (1), 16 binary representation is 10000

The conversion between decimal and binary is a four-step process:

1. Convert the integer part of the decimal system to binary. Factor the decimal number into two factors and take the remainder of it.

For example, 101 2 = 50, the remainder is 1, 50 2 = 25, the remainder is 0, 25 2 = 12, the remainder is 1, 12 2 = 6, the remainder is 0, 6 2 = 3, the remainder is 0, 3 2 = 1, the remainder is 1, 1 2 = 0, and the remainder is 1.

2. Write the corresponding remainder from low to high, as above is 1100101, that is, the binary representation of 101.

3. Convert the decimal part of the decimal system to binary. Multiply the decimal by 2 and round it until there are no decimals. Note that not all decimals can be converted to binary.

For example, take an integer of 1, and take an integer of 1.

4. Put the corresponding integers in order.

To convert a binary number to a decimal number, just count it the other way around.

Human arithmetic uses the decimal system, which may have something to do with the fact that humans have ten fingers. Aristotle claimed that the universal use of the decimal system is simply the result of the anatomical fact that the vast majority of people are born with 10 fingers. In fact, in the written notation system independently developed in the ancient world, almost all of them were decimal except for the wedge-shaped numerals of the Babylonian civilization, which had a decimal system, and the Mayan numerals, which had a base of 20.

However, these decimal notation systems are not bit-based.

Binary is a system of numbers that is widely used in computing technology. Binary data is a number represented by two numbers, 0 and 1. Its cardinal number is 2, the carry rule is "every two into one", and the borrowing rule is "borrow one to become two", which was discovered by Leibniz, a German master of mathematical philosophy in the 18th century.

Current computer systems use basically binary systems, and data is stored in computers mainly in the form of complements. Binary in a computer is a very tiny switch, with "on" for 1 and "off" for 0.

The invention and application of computers, which are known as one of the important symbols of the third scientific and technological revolution in the 20th century, because digital computers can only recognize and process strings of '0' and '1' symbols. The mode of operation is binary. The 19th-century Irish logician George Bull's thought process on logical propositions was translated into pairs of symbols''binary is a carry system that is every 2 digits.

is the base operator. Because it uses only two number symbols, it is very simple and convenient and easy to implement electronically.

Method: Multiply each number of binary defaults by the corresponding power of 2 from right to left, and from left to right after the decimal point.

For example, binary numbers are converted to decimal numbers.

binary) = 1 * 2 0 + 0 * 2 1 + 1 * 2 2 + 1 * 2 3 + 0 * 2 -1 + 1 * 2 -2 = 1 + 0 + 4 + 8 + 0 + decimal).

So to sum up, the general formula is:

.EFG (binary) = d*2 0 + c*2 1 + b*2 2 + a*2 3 + e*2 -1 + f*2 -2 + g*2 -3 (decimal).

Decimal is converted to binary.

Decimal to binary is divided into integer to binary, and decimal to binary.

The whole brother imaginary number turns binary.

Adoption"Divide by 2 and take the remainder and arrange them in reverse order"Law:

1.First, divide a decimal integer by 2 to get a quotient and remainder.

2.Then use 2 to remove the resulting quotient, and you will get a quotient and a remainder.

3.Repeat until the quotient is less than 1.

4.Then arrange all the resulting remainders and reverse them (in reverse order), remembering to do it all the way around.

Decimal to binary.

Adoption"Multiply by 2 and round up, in order"Law:

1.Using 2 times decimal decimals, you can get the product, and the integer part of the product is taken out.

2.Multiply the remaining decimal part by 2 to get another product, and then take out the integer part of the product.

3.Repeat until the decimal part of the product is zero, at which point 0 or 1 is the last digit of binary, or until the required hail is reached.

1. Conversion between decimal and binary (1) Decimal is converted to binary, divided into integer part and decimal part Integer part method: divide by 2 remainder, that is, divide the integer part by 2 each time, the remainder is the number on the bit weight, and the quotient continues to divide by 2, and the remainder is the number on the previous bit weight, this step continues until the quotient is 0, and the last reading, starting from the last remainder reading, all the way to the first remainder. Here's an example:

Example: Convert 168 in decimal to binary to get the result Convert 168 in decimal to binary, (10101000) 2 Analysis: In the first step, divide 168 by 2, quotient 84, and the remainder is 0.

In the second step, divide quotient 84 by 2, and the remainder of quotient 42 is 0. In the third step, divide quotient 42 by 2, and the remainder of quotient 21 is 0. In the fourth step, divide quotient 21 by 2, and the remainder of quotient 10 is 1.

In the fifth step, divide quotient 10 by 2, and the remainder of quotient 5 is 0. In the sixth step, divide quotient 5 by 2, and the remainder of quotient 2 is 1. In the seventh step, divide quotient 2 by 2, and the remainder of quotient 1 is 0.

In the eighth step, divide quotient 1 by 2, and the remainder of quotient 0 is 1. The ninth step, reading, because the last digit is obtained after dividing by 2 many times, because it is the highest digit, the reading number is read forward from the last remainder, that is, 10101000 (2) Decimal part method: multiply by 2 to take the whole number, that is, multiply the decimal part by 2, then take the integer part, and the remaining decimal part continues to multiply by 2, then take the integer part, and multiply the remaining decimal part by 2, until the decimal part is zero.

If it can never be zero, just like rounding decimal numbers, when retaining how many decimal places are required, choose according to whether the next digit is 0 or 1, if it is zero, round off, if it is 1, enter one place. In other words, 0 rounding. The reading should be read from the first integer to the next integer, as shown below

Example 1: Convert to binary to get the result: Convert to binary (analysis:

The first step is to multiply by 2 to obtain, then the integer part is 0 and the decimal part is; The second step is to multiply the decimal part by 2 to get it, then the integer part is 0, and the decimal part is; The third step is to multiply the decimal part by 2 to obtain, then the integer part is 1 and the decimal part is; The fourth step, reading, starts from the first reading and reads to the last digit, that is. The method of converting decimal to binary, you need to pay attention to: 1) Decimal to binary, you need to divide into two parts, integer and decimal number, respectively2) When converting integer, use the remainder method of dividing by 2, and when converting decimals, use multiply by 2 to take the whole number3) Pay attention to the direction of their readingTherefore, from the above method, we can conclude that the decimal number is converted to binary as, or the decimal number is converted to binary number approximately equal.

3) Binary to decimal method of guessing the circle without dividing integers and decimal parts: adding by weight, that is, multiplying the number on each bit of binary by weight, and then adding the sum is the decimal number. Example: Converting binary numbers to decimal numbers.

Binary to decimal.

Method: "Sum by weight".

Example: Rule: The number of digits in the single digit is 0, and the number of digits in the tens digit is 1,..Ascend in turn, and ten.

The number of quantiles is -1, and the number of times of numbers in the percentile is -2,..Descending order.

Note: Not any decimal number can be converted to a binary number with finite digits.

2) Decimal to binary.

Decimal integer to binary number: "divide by 2 to take the remainder, in reverse order" (divide by 2 to take the remainder) Example]:

44÷2 ……It is 0

Decimal numbers, individual digits, respectively： .Thousand, hundred, ten, one .

Binary numbers, each bit of the hidden blue rise, respectively： .Eight, four, two, one...

The rest is up to you, and it's slow to explore.

The decimal number, the old 8031, is: 8 thousand, 0 hundred, 3 ten, 1.

The binary number, 1101, is: 1 eight, 1 four, 0 two, 1 one, i.e. 13 in decimal.

The binary number of 10 is 1010

The specific steps are as follows:

Then write the remainder upside down as 1010.

So the binary number of 10 is 1010.

The decimal to binary conversion method is summarized as follows: divide the number to be converted by 2 until the quotient is 0, and write the remainder upside down.