Decimal to other decimal conversions, other decimal to decimal conversion methods

The decimal number is divisible by other bases, and the resulting remainder is reversed, and the decimal part is multiplied by the other bases until it is an integer. For example, convert the decimal to binary integer part: 24 2=12....0

Then we write the remainder in order from bottom to top: 11000, then this 11000 is the binary form of decimal 24. Decimal part:

Then we write the integer part in order from top to bottom: 101, then this 101 is the binary form of decimal.

So: the conversion of decimal to binary is.

Because the principle of conversion between various base systems is the same, let's take binary as an example, that is, to convert decimal to binary, and binary to decimal.

Because there are integer and decimal parts, so the conversion of integers and decimal numbers is not the same, let's talk about the integer part first, take the decimal number 827 as an example, and convert it to binary.

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The short division method used here is to divide this number by 2, put the remainder at the end, and so on.

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Then arrange the remainder in order from bottom to top to become a binary number, and then convert this number to decimal.

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This process only requires a formula, a direct number, the index of the single digit is 0, and so on, adding it up.

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Let's move on to decimals, for example, here we convert to octal numbers, multiply this decimal by 8, and take the integer part.

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Then multiply the decimal of the number by 8 again to get the integer part, which is arranged in the order in which it was obtained.

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Converting decimal octals to decimal is the opposite process, but -1 and -2.

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Decimal. Integers are converted to other bases, and the remainder is taken by division.

Method: The following is illustrated with an example:

Convert decimal integers to binary numbers.

The divide by 2 reverse remainder method is adopted:

Reading the remainder of each time from the bottom up is the result of the conversion:

Convert decimal 10 integers to hexadecimal numbers, using the reverse remainder method of dividing by 16:

123/16=7...11 (denoted by b) reads the remainder of each time from the bottom up, and this is the result of the conversion:

123=(7b)16

Divide by 12, take the remainder, divide the remaining number by 12, take the remainder, divide until 0, the resulting remainder is in reverse order is the decimal number you want, such as: 100 divided by 12, the remainder is 4, the divided number 8 is divided by 12, the remainder is 8, this decimal number is the language with recursion is very good.

You can use the calculator that comes with your computer to convert between binary and decimal systems, please follow the steps below.

1. Click "All Programs Accessories Calculator" in the start menu of your computer to enter the calculator interface.

2. Then find "Programmer" in the "View" option on the calculator interface, and click on it.

3. Then select the "Decimal" option with the mouse, and click the number 8 button to enter the decimal number 8 in the calculation column

4. Then click the "Binary" option in the interface with the mouse, and you can find that the binary number "1000" of 8 will appear in the calculation column, and you can complete the conversion of decimal number to binary.

5. Then click the "Decimal" option in the interface at this time, and the decimal number "8" of "1000" will appear in the calculation column. Once you have done the above, you can convert between binary and decimal systems.

Binary numbers. Convert to decimal system.

The number is carried out using the method of "multiplication and summing". Based on the fact that the "weight" of one digit to the left of the decimal point (the lowest digit in the case of an integer) is equal to 1, (the lowest digit in the case of an integer), the weight of the digit is equal to the weight of the right neighbor multiplied by 2 for each digit to the left, and the weight of the digit is equal to the weight of the left neighbor multiplied by 2 for each digit to the right. Finally, the number on each bit is multiplied by the corresponding weight of the standard, and finally all of them are accumulated, and the sum obtained is the result of conversion.

For example, to convert a decimal integer to binary, use "divide by two and take the remainder in reverse."

law", for example:

Reading all the remainders from the bottom up is the result of the transformation:

Computer conversion of decimal and binary.

The conversion of binary to decimal is as follows:

The calculation method for converting binary to decimal is as follows: 1. Unsigned integer, from right to left, multiply the number on the binary bit by the sum of the nth power of 2 (n is greater than or equal to 0); 2. Signed binary integers, except for the highest sign bit (1 is a negative number, 0 is a positive number), and the rest is the same as the unsigned binary conversion method to decimal system; 3. The decimal binary is converted into a decimal number, multiply the binary number on the first digit after the decimal point by the negative quadratic square of 2 plus the binary number on the second digit multiplied by the negative quadratic of 2, and so on multiply the binary number on the nth digit by the negative n power of 2.

1. The method of converting unsigned integer binary numbers to decimal numbers.

The binary of an unsigned integer is converted into a decimal number, starting from the first right digit of the binary number, from right to left, first multiply the number in the binary position by the power of the corresponding digits of 2, and then add the product of each bit to get the decimal number corresponding to the binary number.

Example] Convert a binary number 1101001 to a decimal number.

Analysis: Starting from the first digit on the right side of the binary number 1101001, the first digit is 1, then there is 1=1, the second digit is 0, then there is 0=0, the third digit is 0, then there is 0=0, the fourth digit is 1, then there is 1=8, the fifth digit is 0, then there is 0=0, the sixth digit is 1, then there is 1=32, the sixth digit is 1, then there is 1=64.

Add all the products to get 1+0+0+8+0+32+64=105, so the conversion of binary numbers to decimal numbers 1101001 is 105.

2. The method of converting signed binary integers to decimal numbers.

If it is 1, it means that it is a negative number, if it is 0, it means that it is a positive number, and then convert it to a decimal number after determining the symbol.

Example] Convert a signed binary number 10000000 00010000 into a decimal number.

Analysis: The original code of the binary number with signs, the highest bit represents the matching bit, we first observe that the highest bit is 1, which means that this is a negative number, so we can find the decimal number corresponding to this binary number is -(0+0+0+0+1)=-16.

3. The method of converting decimal numbers into decimal numbers.

The method of converting a decimal number from a decimal number to a decimal number is obtained by multiplying the digits on the binary digits by the negative power of 2 from left to right, and then adding all the products together.

How do you convert the decimal part of a decimal number to binary?

Decimal part: Example: *2= *2= Then we write the integer part in order from top to bottom:

101, then this 101 is the binary form of decimal So: (ten) = (two) The decimal system is converted into binary like this: the decimal number is divisible by two, and the resulting remainder is reversed.

For example, converting 10 in decimal to binary is as follows: (1) 10 2, quotient 5 and 0; (2) 5 2, quotient 2 surplus 1; (3) 2 2, quotient 1 surplus 0; (4) 1 2, quotient 0 more than 1(5) If the remainder of the obtained nephew is reversed, it is 1010, so the conversion of 10 in decimal to binary is 1010.

How to convert decimal to binary.

Mutual algorithm for decimal and binary conversions.

Decimal to binary:

Divide by 2 toss until the result is 1

Write the remainder and the last 1 in reverse order from bottom to top is the result.

For example 302302 2 = 151 remainder 0

151 2 = 75 surplus 1

75 2 = 37 remainder 1

37 2 = 18 remainder 1

18 2 = 9 0 remaining

9 2 = 4 remainder 1

4 2 = 2 0 remaining

2 2 = 1 remainder 0

Therefore, binary is 100101110

Binary to decimal.

Starting from the last digit, it is listed as the first. Bit.

The number in the nth place (0 or 1) is multiplied by 2 to the nth power.

The sum of the results obtained is the answer.

For example: 01101011Turn decimal:

Bit 0: 1 times 2 to the power of 0 = 1

1 times 2 to the power of 1 = 2

0 times 2 to the power of 2 = 0

1 times 2 to the 3rd power = 8

0 times 2 to the power of 4 = 0

1 times 2 to the 5th power = 32

1 times 2 to the 6th power = 64

0 times 2 to the power of 7 = 0

Then: 1+2+0

Binary 01101011 = decimal 107