How to convert binary numbers with decimal numbers to decimal numbers, such as 0.011101? I hope you can give me your advice and write down the conversion process

How to convert binary numbers with decimal numbers to decimal numbers, such as 0.011101? I hope you can give me your advice and write down the conversion process

1. Conversion between binary and decimal numbers
(1) Convert binary to decimal
Each binary number is expanded by weight and then summed
2 * 1 + 2 * 1 + 2 * 1 + 2 * 1 + 2 * 1 + 2 * 1 + 2 * 1 + 2 * 1
(2) Convert decimal to binary
Generally, it is necessary to separate the integer part and the decimal part of decimal number
Integral part calculation method: take the remainder by Division 2
The binary value of the decimal number (53) 10 is (110101) 2
The decimal part is calculated by multiplying 2. In other words, the decimal part is multiplied by 2 in each step. The number (0 or 1) to the left of the decimal point of the product is the number in the binary representation, and the integer part obtained by the first multiplication is the highest order
Convert (0.5125) 10 to binary. (0.5125) 10 = (0.101) 2
Additional information follows
1. Decimal system
The decimal system uses ten digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) to count. The base number is 10 and every decimal one
ENIAC, the first electronic digital computer in history, is a decimal machine. Its numbers are expressed in decimal system and operated in decimal form. The design of decimal machine is much more complicated than that of binary machine. However, there are two kinds of stable components in nature, such as on and off of switch, on and off of circuit, high and low voltage, It is very suitable to represent the number in the computer. The design process is simple and reliable. Therefore, it is changed to binary computer
2. Binary
Binary takes 2 as the cardinal number, only 0 and 1 are used to represent the number
Binary follows the same operation rules as decimal numbers, but it is simpler than decimal
(1) Addition: 0 + 0 = 0 0 0 + 1 = 1 1 1 + 0 = 1 1 1 + 1 = 0
(2) Subtraction: 0-0 = 0 1-1 = 0 1-0 = 1 0-1 = 1
(3) Multiplication: 0 * 0 = 0 0 0 * 1 = 0 1 * 0 = 0 1 * 1 = 1
(4) Division: 0 / 1 = 0 1 / 1 = 1, the divisor cannot be 0
3. Octal
The so-called octal is that its base number is 8, and the base value can take 0, 1, 2, 3, 4, 5, 6, 7, a total of 8 values, every eight into one
Octal and decimal operation rules are the same. So why use octal? Is it necessary to design octal computer? In fact, octal and hexadecimal are mainly used for convenience of writing and expression, because the number of binary representation is relatively long, More importantly, because there is a kind of equivalence between binary and octal, every three binary is exactly equal to one octal number (23 = 8). Therefore, there is no difference in operation between binary system and decimal system, but time base does not have this advantage
4. Hexadecimal
Hexadecimal is a more compact representation of the hexadecimal system, which is also a widely used method for users
The cardinal numbers are: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, a, B, C, D, e, F, every decimal one. In the hexadecimal system, numbers from 10 to 15 are represented by a, B, C, D, e, F, respectively
Binary number and its equivalent octal, decimal and hexadecimal numbers
Binary octal decimal hexadecimal
0000 0 0 0
0001 1 1 1
0010 2 2 2
0011 3 3 3
0100 4 4 4
0101 5 5 5
0110 6 6 6
0111 7 7 7
1000 10 8 8
1001 11 9 9
1010 12 10 A
1011 13 11 B
1100 14 12 C
1101 15 13 D
1110 16 14 E
1111 17 15 F
2、 Base conversion
1. Conversion between binary and decimal numbers
(1) Convert binary to decimal
Each binary number is expanded by weight and then summed
The binary number (101.101) 2 = 1 * 22 + 0 * 21 + 1 * 20 + 1 * 2-1 + 0 * 2-2 + 1 * 2-3 = (5.625) 10
(2) Convert decimal to binary
Generally, it is necessary to separate the integer part and the decimal part of decimal number
Integral part calculation method: take the remainder by Division 2
The binary value of the decimal number (53) 10 is (110101) 2
The decimal part is calculated by multiplying 2. In other words, the decimal part is multiplied by 2 in each step. The number (0 or 1) to the left of the decimal point of the product is the number in the binary representation, and the integer part obtained by the first multiplication is the highest order
Convert (0.5125) 10 to binary. (0.5125) 10 = (0.101) 2
2. Conversion between octal, hexadecimal and hexadecimal
The conversion method between octal, hexadecimal and hexadecimal is similar to that of binary and decimal
（73）8=7*81+3=（59）10
（0.56）8=5*8-1+6*8-2=(0.71875)10
(12A)16=1*162+2*161+A*160=(298)10
(0.3C8)16=3*16-1+12*16-2+8*16-3=(0.142578125)10
Decimal integer →→→→→ octal method: "take remainder by division 8"
Decimal integer →→→→→ hexadecimal method: get remainder by division 16
（171）10=（253）8
（2653）10=（A5D）16
Decimal decimal →→→→ → octal decimal method: "multiply 8 to get the whole"
Decimal decimal →→→→→ hexadecimal decimal method: multiply 16 to get the whole number
（0.71875）10=（0.56）8
(0.142578125)10=(0.3C8)16
3. Conversion between non decimal numbers
(1) Conversion between binary number and octal number
The conversion method is as follows: take the decimal point as the boundary, synthesize one octal number for each three binary numbers on the left and right, or expand each octal number into three binary numbers, and add 0 if less than three digits
（423.45）8=（100 010 011.100 101）2
（1001001.1101）2=（001 001 001.110 100）2=（111.64）8
2. Binary to hexadecimal conversion
Conversion method: take the decimal point as the boundary, synthesize one hexadecimal number from each four digit binary to the left and right, or expand each hexadecimal number into four binary numbers, and add 0 if less than four digits
( ABCD.EF ）16=（1010 1011 1100 1101.1110 1111）2
（101101101001011.01101）2=（0101 1011 0100 1011.0110 1000）2=（5B4B.68）16
Conversion is not to understand, read more will! I am also learning computer, written examination when the system conversion
We should be familiar with these methods!

How to convert decimal to binary

Multiply the decimal part by 2, and take the integer part of the result as one bit of binary. Then continue to multiply the decimal part of the result by 2 until all the decimal parts are 0 (there may be endless loop multiplication). For example: 0.8125 is replaced by binary, as follows: 0.8125x2 = 1.625... 10.62

Decimal conversion of binary system 22.8125 to binary

The integer is divided by 2, and the quotient is divided by 2 to get 0. The remainder is arranged in reverse order. 22 / 2 11 + 011 / 25 + 15 / 22 + 12 / 21 + 01 / 20 + 1, so the binary of 22 is 10110 decimal multiplied by 2, rounded, and the decimal part is multiplied by 2, rounded, until the small part 0 is obtained

1011 in the binary system is equivalent to () in the decimal system? The number in the binary system () is equivalent to 8 in the decimal system

The procedure is 1011 = 2 ^ 3 + 2 ^ 1 + 2 ^ 0 = 8 + 2 + 1 = 11

The number 101011 in the binary system is equal to which number in the decimal system?

431 + 2 + 0 + 8 + 0 + 32 = 43 can you see how to calculate? According to the sum of power 2 and 1 * 2 ^ 5 + 0 * 2 ^ 4 + 1 * 2 ^ 3 + 0 * 2 ^ 2 + 1 * 2 ^ 1 + 1 * 2 ^ 0 = 43, I teach you the following methods: 1. Open the calculator on the computer (method: start → accessories → calculator). 2. Click "view" menu → select: "scientific" 3. Select "binary"

What number in decimal is equal to 1101 in binary system

1101 ==> 8 + 4 + 0 + 1 = 13

Which number in decimal is 1101 in binary system

1101 is 1 * 2 ^ 0 + 0 * 2 ^ 1 + 1 * 2 ^ 2 + 1 * 2 ^ 3 = 13

How to calculate the conversion of binary number to decimal number?

For example, 10100101, where 2 ^ 2 refers to the second power of 2. You should pay attention to the rule that the exponent is 0-7, and the middle is 2 (because of the binary system). The value in the front is the same as that of the binary number, and the hexadecimal and octal are also similar
1 0 1 0 0 1 0 1
1*2^7 + 0*2^6 + 1*2^5 + 0*2^4 + 0*2^3 + 1*2^2 + 0*2^1 + 1*2^0
128 + 0 + 32 + 0 + 0 + 4 + 0 + 1 =165

. convert decimal to binary: (17) 10 = () 2   A. 10000001      B. 00010001       C. 01000001        D. 10001000

17 / 2 = 8 + 1, so the last 1,8 / 2 = 4 + 0, so the 2 bits are 0,4 / 2 = 2 + 0,2 / 2 = 1 + 0,1 / 2 = 0 + 1
So it's 00010001

Convert a binary number to a decimal number Convert the following binary numbers: to decimal ten thousand one hundred and one one hundred and ten thousand and one ten thousand and one one thousand one hundred and eleven one million one hundred and one thousand one hundred and ten

, 110001 = 1 × 2 ^ 4 + 0 × 2 ^ 4 + 0 × 2 ^ 3 + 1 × 2 ^ 3 + 1 × 2 ^ 2 + 0 × 2 ^ 3 + 1 × 2 ^ 3 + 0 × 2 ^ 5 + 1 × 2 ^ 4 + 0 × 2 ^ 3 + 0 × 2 ^ 2 + 0 × 2 ^ 2 + 0 × 2 ^ 1 + 1 × 2 ^ 0 = 4910001 = 1 × 2 ^ 4 + 0 × 2 ^ 4 + 0 × 2 ^ 1 + 1 × 2 ^ 0 = 4910001 = 1 × 2 ^ 4 + 0 × 2 ^ 3 + 0 × 2 ^ 2 + 0 × 2 ^ 1 + 1 × 2 ^ 0 = 171111 = 1 × 2 ^ 3 + 1 × 2 ^ 2 + 1 × 2 ^ 1 + 1 × 2 ^ 1 + 1 × 2 ^ 0 = 151101110 = 1 × 2 = 1 × 2 = 1 × 2 = 1 × ^ 6 + 1