# Binary to decimal calculation process in detail

### Binary to decimal, how to calculate ？？？？？？？？？？？

Binary to decimal conversion: the base is multiplied by the power, and then added, simplifying the operation can be left out of the term where the number of digits is 0, (because 0 multiplied by any other number that is not 0 is 0). The decimal part is the same, but with less precision.

Method: “Expanding the sum by power”

Example: 10001111

1×2⁷+1×2³+1×2²+1×2¹+1×2⁰=143, so the decimal representation of 10001111 is 143.

The rule: the number of digits in the single digit is 0, the number of digits in the tens digit is 1, …… , in increasing order, while the number of times the number in the tenths place is -1 and the number of times the number in the hundredths place is -2, …… , in decreasing order.

### Binary to decimal conversion steps?

Method 1: from right to left with each number of binary to multiply by the appropriate power of 2, after the decimal point is from left to right

Example: binary number 1101.01 converted to decimal

1101.01 (2)

=1*2  +0*2  +1*2  +1*2  +1*2 [-1] + 0*2 [-2]

=1+0+4+8+0+0.25=13.25 (10)

This is the first time that a binary number is converted to decimal. +1*2 [-2]

=1+0+4+8+0+0+0.25=13.25 (10)

Method 2: The binary number is first written as a weighted coefficient expansion, and then summed according to the rules of decimal addition. This is called the “weighted sum” method.

For binary numbers with n integers and m decimals, the weighted coefficients are expressed as follows: N(2) = an-1×2n-1+an-2×2n-2+……+a1×21+a0×20+a-1×2-1+a-2×2-2+……+a-m×2-2+a-m×2-2 ……+a-m×2-m (10) where aj denotes the coefficient in the jth place, which is one of 0 and 1.

Example: binary number 1101 converted to decimal

1101 (2)

=1*2  + 1*2  + 0*2  + 1*2 

=13 (10)

Note:

1, [] the number in parentheses represent the sub-square, such as  for the second square, [-1] is negative primary.

2. The number in the () bracket represents the decimal number, (2) is binary, (10) is decimal.

### Binary to decimal method

Binary to decimal method is as follows:

1, the unsigned integer binary into decimal numbers, from the first bit of the right side of the binary number, from right to left, the first binary position multiplied by the number of the corresponding digit of the power of 2, and then add the product of each can be obtained by the binary number of the corresponding decimal number.

2, with the sign of the binary number into decimal numbers, first observe the binary number of the highest bit is what number, if it is 1, that is, the negative number, if it is 0, that is, the positive number, to determine the sign of the decimal number and then converted to decimal numbers.

3, the decimal number of binary numbers into decimal numbers, from left to right, with the number of binary digits multiplied by 2 to the power of the negative number of digits, and then add all the products can be obtained.

Binary to decimal:

Binary to decimal is the use of certain mathematical means to convert the binary digits into decimal digits, widely used in programming and other fields.

Binary is a number system widely used in computing technology. Binary data is a number represented by two digits, 0 and 1. Its base is 2, the rule of rounding is “two into one”, and the rule of borrowing is “borrowing one as two”.

The decimal system is a method of counting. The use of decimal system in human arithmetic may be related to the fact that humans have ten fingers. Aristotle claimed that the universal use of the decimal system was simply a result of the anatomical fact that the vast majority of humans are born with 10 fingers.

### How to convert binary to decimal

First of all, let’s take an example: decimal 123 = 1 * 100 + 2 * 10 + 3 * 1, where 100 is 10 squared, 10 is 10 to the first power, 1 is 10 to the zero power, respectively, in the hundredths, tenths, and digits, which is also called the bit weights of the corresponding positions, then binary is also the same reason.

Binary to decimal conversion is: the binary number in each position multiplied by the bit weights in the position, and then add. Such as 101101 converted to decimal is 1 * 2 of the 5th + 0 * 2 of the 4th + 1 * 2 of the 3rd + 1 * 2 of the 2nd + 0 * 2 of the 1st + 1 * 2 of the 0th = 32 + 8 + 4 + 1 = 45; this 45 is the corresponding decimal number.

### Binary how to convert decimal

Binary is divided into two categories of integer binary and decimal binary, the two binary into decimal is converted to the practice of summing by weighted expansion. The next step is to explain in detail.

Integer binary to decimal conversion example: the binary bit 1010 into decimal.

The first step: the first 1010 complement to 8 bits, that is, 00001010.

The second step: as the first digit is 0 for positive, then the algorithm is shown below.

Step 3: Calculate the result, the result is 10, that is, 1010 is converted to decimal as 10.

Decimal binary conversion to decimal

Example: convert 1011.01 to decimal.

Step 1: The algorithm is shown below.

Step 2: The result of the calculation is 11.25, i.e. the result of converting 1011.01 to decimal is 11.25.

Decimal to binary

Example: convert decimal to 42 to binary. The method of converting decimal to binary is “divide by two and take the remainder”.

Step 1: 42/2=21……0

21/2=10……0

10/2=5……0

5/2=2……0

2/2=1……0

1/2=0……1

Step 2: So 42 corresponds to the to the binary bit 101010.

### How do you count binary to decimal conversion?

The decimal numbers, the individual bits, are… Thousands, Hundreds, Tens, Individuals….

Binary numbers, individual bits, are:… Eight, four, two, one…..

The other bits, it’s up to you, just to figure it out.

The decimal number, 8031, is: 8 thousands, 0 hundreds, 3 tens, 1 one.

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