How to convert an integer to binary

2) Integer part: The 2 (x) that appears below indicates the meaning of 2 to the x power.

Decimal part: so: (two) = (ten).

Binary. Convert to decimal system.

Here's how you can use the 8421 code method This method is to count the binary you want to convert from right to left, start counting from 0 (this number is called n), stop where the number is 1, and multiply 1 by 2 to the nth power, and finally add these 1 times 2 to the n power, which is the decimal system of this binary number

Let's take an example:

Finding the decimal number of 110101 starts from right to left.

1 times 2 to the power of 0, equal to 1;

1 times 2 to the 2nd power, equal to 4;

1 times 2 to the 4th power, equal to 16;

1 times 2 to the 5th power, equal to 32;

Add these results together: 1 4 16 32 53

Positive integers are converted to binary. The main point must be remembered: divide by two to take the remainder, and then arrange it in reverse order, and fill in zero in the high position.

That is to say, divide the positive decimal number by two, divide the obtained quotient by two, and so on until the quotient is zero or a while, and then mark the remainder of each step next to it, and finally write it backwards, and it is OK to fill zero in the high position. Heck, let's give an example, such as 42 to binary, as shown in the link.

Convert positive integers to binary calculations: divide the positive integer by two, divide the quotient by two until the quotient is 1 or 0, and then write the remainder from the bottom up to get the binary value.

The specific calculation method for converting a decimal positive integer 18 to a binary number is as follows:

18 2=9 remainder 0;

9 2=4 remainder 1;

4 2=2 remainder 0;

2 2=1 remainder 0;

1 2=0 remainder 1;

Write the above remainder results in reverse order and convert them into binary, which is: 10010;

The format of the standard writing is: (18)10=(10010)2;

How to convert decimals to binary numbers:1. The decimal part is converted to binary, mainly the decimal part is multiplied by 2, and the integer part is placed after the decimal point from left to right until it is 0 after the decimal point. For example, in decimal format, you want to convert it to a decimal in binary.

2. Convert to binary, multiply the decimal part by 2 to obtain, and then take the integer part 0.

3. Multiply the decimal part by 2 to get, and then take the integer part 0.

4. Multiply the decimal part by 2 to get 1, and then take the integer part 1.

5. The result of the binary obtained is.

Counting systemBase. In the notation system at the position of the cardinal number b (where b is a positive natural number, called the cardinal number), the b basic symbols (or numbers) correspond to the smallest b natural numbers including 0. To produce other numbers, the position of the symbol in the number is used.

The sign of the last digit is multiplied by b by its value in the left digit with its own value.

Binary count.

Leibniz, a German mathematician from the 17th to the 18th century, was the first person in the world to propose binary notation. With binary notation, only the two symbols 0 and 1 are used, and no other symbols are needed.

4 (decimal) = 100 (binary).

Convert a decimal integer to a binary exposition integer:

Decimal integers are converted to binary integers"Divide by 2 and take the remainder and arrange them in reverse order"Law. Here's how: divide a decimal integer by 2 to get a quotient and remainder.

Removing the quotient with 2 will give a quotient and remainder again, and so on until the quotient is less than 1, and then the remainder obtained first will be used as the lower significant digit of the binary number, and the remainder obtained later will be used as the high significant digit of the binary number, and then arranged in turn.

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 two to take the remainder) [Example]:

You write a small program, input decimal, output binary.

That's it.

Binary refers to the number system based on 2 in mathematical and numerical circuits, and the binary system that represents the system based on 2. So how do integer conversions turn into binary?

1. Take the decimal number 101 as an example, through short division, take 2 as the divisor, divide 101 by 2, you can get the quotient of 50, and at the same time get the remainder of 1.

2. Use the forest quotient 50 obtained in the first step as the dividend, and continue to use 2 as the divisor, you can get the quotient 25, and get the remainder 0 at the same time.

3. Using the quotient 25 in the second step as the dividend and 2 as the divisor, you can get the quotient 12 and the remainder 1.

4. Repeat the above steps by analogy, until the final quotient is less than 2. Get the remainder separately.

5. You can see that there are a total of 6 remainders, respectively, arrange all the remainders from bottom to top to get the binary number 100101 of 101.

That's all there is to know about how integer conversion can be converted into binary.

Answer: Decimal 127 is converted to binary which is equal to 0b11111111.

The solution steps are as follows:

127÷2=63…The remainder 1,1 2 0=1,63 2=31....The remainder 1,1 2 1=2,31 2=15....The remainder is 1,1 2 2 = 4,15 2 = 7....The remainder 1,1 2 3=8,7 2=3....The remainder of the beats is 1,1 2 4=16,3 2=1....The remainder 1,1 2 5=32,1 2=0....The remainder 1,1 2 6=64, validation: 64 + 32 + 16 + 8 + 4 + 2 + 1 = 127, gets: (127) 1111111).