# How to write a binary to decimal conversion table

### How to convert binary number to decimal number?

In performing a binary to decimal conversion, you can write a table like the one shown above, where the second row writes the binary numbers in order from right to left, the third row writes the product of the second row and the first row, and the fourth row writes the result of adding the values of the third row. The result of the fourth row written in this way is the decimal counterpart of the second binary row.

Binary numbers (binaries) is a 2-digit system, 0, 1 is the basic operator; the basis of computer arithmetic using binary. Computers are based on binary.

In the early design of the common system is mainly decimal (because we have ten fingers, so the decimal system is a more reasonable choice, with the finger can represent ten numbers, the concept of 0 until long after the emergence of the concept, so it is 1-10 instead of 0-9).

After the advent of electronic computers, it was too complicated to use electron tubes to represent the ten states, so there are only two basic states in all electronic computers, on and off. In other words, the two states of the electron tube dictated that electronic computers based on the electron tube use binary to represent numbers and data.

Commonly used binary and 8 and hexadecimal, in computer science, often use hexadecimal, and the use of decimal is very little, this is because of the hexadecimal and binary have a natural connection: 4 binary bits can represent the number from 0 to 15, which is just 1 hexadecimal bit can represent the data, that is, the binary will be converted to 16 as long as the every 4 bit to convert.

### 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] +0*2 [1] +1*2 [2] +1*2 [3] +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 [3] + 1*2 [2] + 0*2 [1] + 1*2 [0]

=13 (10)

Note:

1, [] the number in parentheses represent the sub-square, such as [2] for the second square, [-1] is negative primary.

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

### How to convert binary number to decimal number?

Integer part:

Binary number is converted to decimal number, 2 for the power, from the first place to the left of the decimal point, start labeled with the exponent of 2, starting from 0, 2 to the 0th power, 2 to the 1th power, 2 to the 2th power, and all the way to the far left.

The number on the binary digit is multiplied by the power of the exponent labeled (2 as the base), and then all are added up to sum, and the result is the decimal number converted.

Example: 11010[binary]=1X2^4+1X2^3+0X2^2+1X2^1+0X2^0=26[decimal]

Decimal part:

1, binary decimal converted to decimal is mainly multiplied by the negative 2 times, starting from the decimal point, in turn, multiplied by the negative 2 times, the negative 2 twice, the negative 3 times, and so on. Negative third party, etc.. For example, the binary number 0.001 is converted to decimal.

2, the first bit of 0, then 0 * 1/2, that is, 0 multiplied by 2 minus a square.

3, the second bit is 0, then 0 * 1/4, that is, 0 multiplied by 2 negative quadratic.

4. If the third digit is 1, then 1*1/8, i.e. 1 multiplied by the negative third power of 2.

5, after multiplying each bit, add up, 0 * 1/2 + 0 * 1/4 + 1 * 1/8 to get the decimal 0.125

### How to convert binary to decimal and represent?

“Binary to decimal, decimal to binary algorithm introduction

Decimal to binary:

Roll over and divide by 2 until the result is 1

Write the remainder and the last 1 in reverse chronological order from the bottom to the top

That is the result

For example: 302 converted to binary

302/2

=

151

Remainder 0

151/2

=

75

Remainder 1

75/2

=

37

Remainder 1

37/2

=

18

Remainder 1

18/2

=

9

Remainder 0

9/2

=

4

Remainder 1

4/2

=

2

Remainder 0

2/2

=<

1

Remainder 0

So the binary is 100101110

Binary to decimal

Counting from the last digit, the numbers are listed as the 0th, 1th, 2th,… The nth digit (0 or 1) multiplied by 2 to the nth power adds up to the answer

Example:01101011.to decimal:

0th digit:1 times 2 to the 0th power = 1

1 times 2 to the 1th power = 2

0 times 2 to the 2th power = 0

1 times 2 to the 3rd power = 8

0 times 2 to the 4th power = 0

0 times 4 times 2 = 0

1 times 2 times 5 = 32

1 times 2 times 6 = 64

0 times 2 times 7 = 0

After that: 1 + 2 + 0 + 8 + 0 + 32 + 64 + 0 = 107.

Binary 01101011 = decimal 107.”

### What is the method to convert binary to decimal?

Binary numbers into decimal numbers

Binary 1101 into decimal 1101 (2) = 1 * 2 ^ 0 + 0 * 2 ^ 1 + 1 * 2 ^ 2 + 1 * 2 ^ 3 = 1 + 0 + 4 + 8 = 13 converted to decimal to the right to the left with the number of each of the binary to multiply by the corresponding second power of the 2, but the second power should be from the beginning of the 0 Instead of dividing the 13 decimal by 2 each divided by the remainder will be recorded next to the last by the remainder from bottom to top can be obtained 1101 decimal to binary: with 2 over and over division to the result of 1 will be the remainder and the last 1 from bottom to top in reverse order is the result of, for example, 302302/2 = 151 more than 0151/2 = 75 more than 175/2 = 37 more than 137/2 = 18 more than 118/2 = 9 more than 09 / 2 = 4 more than 14 /2=2 more than 02/2=1 more than 0, so the binary is 100101110 binary to decimal from the last bit to start counting, listed in order as the first 0, 1, 2 … The nth bit of the number (0 or 1) multiplied by 2 to the nth power to get the result of the sum is the answer, for example: 01101011. to decimal: the 0th bit: 1 times 2 of the 0th power = 11 times 2 of the 1th power = 20 times 2 of the 2th power = 01 times 2 of the 3rd power = 80 times 2 of the 4th power = 01 times 2 of the 5th power = 321 times 2 of the 6th power = 640 times 2 of the 7th power = 0 and then: 1 + 2 + 0 + 8 + 0 + 0 + 32 + 64 + 0 = 107. binary 01101011 = decimal 107. binary number is converted to decimal number of the basic practice is that the binary number is first written as a weighted coefficient of expansion, and then summed according to the rules of decimal addition. This practice is called “weighted” method.

Binary to decimal