Regarding the mathematical principle of dividing 2 remainder, what is dividing 2 remainder method

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The remainder method of dividing by 2 refers to converting decimal numbers into binary numbers.

For example, convert 89 to a binary number

89 divided by 2 equals 44 and 1;

44 divided by 2 equals 22 and 0;

22 divided by 2 equals 11 and 0;

11 divided by 2 equals 5 and 1 remains;

5 divided by 2 equals 2 and 1 remains;

2 divided by 2 equals 1 and 0;

1 divided by 2 equals 0 and 1;

Sort the remainder from bottom to top: 1011001, so the binary expression for 89 is 1011001.

The divide-by-two remainder method is mainly used to convert decimal numbers into binary numbers.

For example, convert 89 to a binary number

89 2=44 remainder 1

44 2=22 remainder 0

22 2=11 remainder 0

11 2=5 remainder 1

5 2=2 remainder 1

2 2=1 remainder 0

1 2=0 remainder 1

Then sort the remainders from bottom to top.

This turns 89 into a binary number.

Take 45, for example.

Divide 45 by 2 to get 22 and 1

Divide 22 by 2 to get 11 and 0

Divide 11 by 2 to get 5 and 1

Divide 5 by 2 to get 2 and 1

Divide 2 by 2 to get 1 and 0

Divide 1 by 2 to get 0 and 1

The result is 101101 the other way around

And then derived. 1 2 5 plus 0 2 4 plus 1 2 3 plus 1 2 2 plus 0 2 1 plus 1 2 0 = 45

Comparing the decimal system can understand the meaning of each digit, 2 x is equivalent to 10 x in the decimal system, so as long as you get the multiplier before 2 x in the above equation, you can get the corresponding binary number, and the remainder of the division is for this purpose.

It can be seen that the dividend of the next formula in the above formulas is the result of the previous formula, so to the last equation 1 divided by 2 to get 0 remainder 1, this 1 has actually been divided by 5 2s, and the remainders of the first few formulas are also divided by x 2s, so they are actually the multipliers in front of 2 x and this is probably it.

This is decimal to binary, that is, to keep dividing the quotient by 2 until the quotient is 0, and output the remainder in reverse order, for example.

221 2 110 more than 1

110 2 55 surplus 0

55 2 27 surplus 1

27 2 13 1

13 2 6 surplus 1

6 2 3 0

3 2 1 surplus 1

1 2=0 remainder 1

So the result is 11011101.

Divide that number by two, and how much is left is the answer. It only needs to be divided once.

The divide-by-two remainder method is mainly used to convert decimal numbers into binary numbers.

For example, convert 89 to a binary number

89 2=44 remainder 1

44 2=22 remainder 0

22 2=11 remainder 0

11 2=5 remainder 1

5 2=2 remainder 1

2 2=1 remainder 0

1 2=0 remainder 1

Then sort the remainders from bottom to top.

This turns 89 into a binary number.

The divide-by-two remainder method is mainly used to convert decimal numbers into binary numbers.

For example, convert 89 to a binary number

89 2=44 remainder 1

44 2=22 remainder 0

22 2=11 remainder 0

11 2=5 remainder 1

5 2=2 remainder 1

2 2=1 remainder 0

1 2=0 remainder 1

Then sort the remainders from bottom to top.

This turns 89 into a binary number.

The divide-by-two remainder method is mainly used to convert decimal numbers into binary numbers.

For example, convert 89 to a binary number

89 2=44 remainder 1

44 2=22 remainder 0

22 2=11 remainder 0

11 2=5 remainder 1

5 2=2 remainder 1

2 2=1 remainder 0

1 2=0 remainder 1

Then sort the remainders from bottom to top.

This turns 89 into a binary number.

The divide-by-two remainder method is mainly used to convert decimal numbers into binary numbers.

For example, convert 89 to a binary number

89 2=44 remainder 1

44 2=22 remainder 0

22 2=11 remainder 0

11 2=5 remainder 1

5 2=2 remainder 1

2 2=1 remainder 0

1 2=0 remainder 1

Then sort the remainders from bottom to top.

This turns 89 into a binary number.

Remainder is a term used in division, the remainder refers to the part of the integer division that is not fully divided, and the value of the remainder is between 0 and the divisor (excluding the divisor of the Zheng bracket of the Zhou family).

In the division of integers, there are only two cases: divisible and indivisible. When it is not divisible, a remainder is generated, and the remainder is calculated a mod b = c (b is not 0) means that the remainder obtained by dividing the integer a by the integer b is c. For example:

7÷3 = 2…1, more technical notation can also be written 7 3=2 and 1 3, or 7 mod 3=1.

Division Properties:

1) The absolute value of the difference between the remainder and the divisor should be less than the absolute value of the divisor (applicable to the field of real numbers);

2) Dividend = Divisor Quotient + Remainder; divisor = (dividend - remainder) quotient; quotient = (dividend - remainder) divisor; Remainder = Dividend - Divisor Quotient.

3) If the remainder of a, b divided by c is the same, then the difference between a and b is divisible by c. For example, the remainder of 17 and 11 divided by 3 is 2, so 17-11 is divisible by 3.

4) The remainder of a and b and divided by c (except in the absence of a remainder in the case of a and b) is equal to the sum of the remainder of a and b divided by c respectively (or the remainder of this sum divided by c).

5) The product of a and b divided by the remainder of c is equal to the product of a, b divided by the remainder of c (or the remainder of this product divided by c).