Application of rules in mathematics: binary number system - number translation. Quickly convert a number from the decimal number system to binary
Note 1
If you want to convert a number from one number system to another, then it is more convenient to first convert it to the decimal number system, and only then convert it from the decimal number system to any other number system.
Rules for converting numbers from any number system to decimal
In computing technology that uses machine arithmetic, the conversion of numbers from one number system to another plays an important role. Below we give the basic rules for such transformations (translations).
When converting a binary number to a decimal, you need to represent the binary number as a polynomial, each element of which is represented as the product of a digit of the number and the corresponding power of the base number, in this case $2$, and then you need to calculate the polynomial using the rules of decimal arithmetic:
$X_2=A_n \cdot 2^(n-1) + A_(n-1) \cdot 2^(n-2) + A_(n-2) \cdot 2^(n-3) + ... + A_2 \cdot 2^1 + A_1 \cdot 2^0$
Figure 1. Table 1
Example 1
Convert the number $11110101_2$ to the decimal number system.
Solution. Using the given table of $1$ powers of the base $2$, we represent the number as a polynomial:
$11110101_2 = 1 \cdot 27 + 1 \cdot 26 + 1 \cdot 25 + 1 \cdot 24 + 0 \cdot 23 + 1 \cdot 22 + 0 \cdot 21 + 1 \cdot 20 = 128 + 64 + 32 + 16 + 0 + 4 + 0 + 1 = 245_(10)$
To convert a number from the octal number system to the decimal number system, you need to represent it as a polynomial, each element of which is represented as the product of a digit of the number and the corresponding power of the base number, in this case $8$, and then you need to calculate the polynomial according to the rules of decimal arithmetic:
$X_8 = A_n \cdot 8^(n-1) + A_(n-1) \cdot 8^(n-2) + A_(n-2) \cdot 8^(n-3) + ... + A_2 \cdot 8^1 + A_1 \cdot 8^0$
Figure 2. Table 2
Example 2
Convert the number $75013_8$ to the decimal number system.
Solution. Using the given table of $2$ powers of the base $8$, we represent the number as a polynomial:
$75013_8 = 7\cdot 8^4 + 5 \cdot 8^3 + 0 \cdot 8^2 + 1 \cdot 8^1 + 3 \cdot 8^0 = 31243_(10)$
To convert a number from hexadecimal to decimal, you need to represent it as a polynomial, each element of which is represented as the product of a digit of the number and the corresponding power of the base number, in this case $16$, and then you need to calculate the polynomial according to the rules of decimal arithmetic:
$X_(16) = A_n \cdot 16^(n-1) + A_(n-1) \cdot 16^(n-2) + A_(n-2) \cdot 16^(n-3) + . .. + A_2 \cdot 16^1 + A_1 \cdot 16^0$
Figure 3. Table 3
Example 3
Convert the number $FFA2_(16)$ to the decimal number system.
Solution. Using the given table of $3$ powers of the base $8$, we represent the number as a polynomial:
$FFA2_(16) = 15 \cdot 16^3 + 15 \cdot 16^2 + 10 \cdot 16^1 + 2 \cdot 16^0 =61440 + 3840 + 160 + 2 = 65442_(10)$
Rules for converting numbers from the decimal number system to another
- To convert a number from the decimal number system to the binary system, it must be sequentially divided by $2$ until there is a remainder less than or equal to $1$. A number in the binary system is represented as a sequence of the last result of division and the remainders from division in reverse order.
Example 4
Convert the number $22_(10)$ to the binary number system.
Solution:
Figure 4.
$22_{10} = 10110_2$
- To convert a number from the decimal number system to octal, it must be sequentially divided by $8$ until there is a remainder less than or equal to $7$. A number in the octal number system is represented as a sequence of digits of the last division result and the remainders from the division in reverse order.
Example 5
Convert the number $571_(10)$ to the octal number system.
Solution:
Figure 5.
$571_{10} = 1073_8$
- To convert a number from the decimal number system to the hexadecimal system, it must be successively divided by $16$ until there is a remainder less than or equal to $15$. A number in the hexadecimal system is represented as a sequence of digits of the last division result and the remainder of the division in reverse order.
Example 6
Convert the number $7467_(10)$ to hexadecimal number system.
Solution:
Figure 6.
$7467_(10) = 1D2B_(16)$
In order to convert a proper fraction from a decimal number system to a non-decimal number system, it is necessary to sequentially multiply the fractional part of the number being converted by the base of the system to which it needs to be converted. Fractions in the new system will be represented as whole parts of products, starting with the first.
For example: $0.3125_((10))$ in octal number system will look like $0.24_((8))$.
In this case, you may encounter a problem when a finite decimal fraction can correspond to an infinite (periodic) fraction in the non-decimal number system. In this case, the number of digits in the fraction represented in the new system will depend on the required accuracy. It should also be noted that integers remain integers, and proper fractions remain fractions in any number system.
Rules for converting numbers from a binary number system to another
- To convert a number from the binary number system to octal, it must be divided into triads (triples of digits), starting with the least significant digit, if necessary, adding zeros to the leading triad, then replace each triad with the corresponding octal digit according to Table 4.
Figure 7. Table 4
Example 7
Convert the number $1001011_2$ to the octal number system.
Solution. Using Table 4, we convert the number from the binary number system to octal:
$001 001 011_2 = 113_8$
- To convert a number from the binary number system to hexadecimal, it should be divided into tetrads (four digits), starting with the least significant digit, if necessary, adding zeros to the most significant tetrad, then replace each tetrad with the corresponding octal digit according to Table 4.
Using the familiar decimal system in computer documentation and programming is very inconvenient. Conversions from binary to decimal systems and vice versa are very labor-intensive processes.
The origin of the octal system, as well as the decimal system, is associated with counting on fingers. But it is not the fingers that need to be counted, but the spaces between them. There are just eight of them.
The solution to the problem was octal. At least at the dawn of computer technology. When the processor capacity was small. The octal system made it easy to convert both binary numbers into octal and vice versa.
The octal number system is a number system with a base of 8. It uses the numbers from 0 to 7 to represent numbers.
Conversion
To convert a number to binary, you need to replace each digit of the octal number with a triple of binary digits. It is only important to remember which binary combination corresponds to the digits of the number. There are very few of them. Only eight!In all number systems, except decimal, the digits are read one at a time. For example, in the octal system the number 610 is pronounced "six, one, zero."
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The components of electronic machines, which include computers, have only two distinguishable states: there is current and there is no current. They are designated "1" and "0" respectively. Since there are only two such states, many processes and operations in electronics can be described using binary numbers.
Instructions
Divide the decimal number by two until you get a remainder indivisible by two. At the step we get the remainder 1 (if the number was odd) or 0 (if the dividend is divisible by two without a remainder). All these balances must be taken into account. The last quotient obtained as a result of such step-by-step division will always be one.
We write the last unit in the most significant digit of the desired binary, and write the remainders obtained in the process after this unit in reverse order. Here you need to be careful and not skip zeros.
Thus, the number 235 in binary code will correspond to the number 11101011.
Now let's convert the fractional part of the decimal number into the binary number system. To do this, we sequentially multiply the fractional part of the number by 2 and fix the integers of the resulting numbers. We add these integer parts to the number obtained in the previous step after the binary one in direct order.
Then the decimal fraction 235.62 corresponds to the binary fraction 11101011.100111.
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note
The binary fractional part of a number will be finite only if the fractional part of the original number is finite and ends in 5. The simplest case: 0.5 x 2 = 1, therefore 0.5 in the decimal system is 0.1 in the binary system.
Sources:
- Converting decimal numbers to binary in 2019
Tip 4: How to convert binary numbers to decimal
The binary or binary number system is used to display electronic information. Any number can be written in binary form. The binary system is used in all computers. Each entry in them is encoded according to certain rules using a set of two characters: 0 and 1. You can convert a binary number into its decimal representation, which is more convenient for the user, using the developed algorithm.
Instructions
Imagine the number as powers of 2. To do this, all eight digits are sequentially multiplied by the number 2 raised to . The degree must correspond to the digit category. The digit is counted from zero, starting from the least significant, rightmost symbol of the binary numbers. Write all eight composed works in .
Tip 5: How to write a decimal number in the binary number system
Decimal system dead reckoning– one of the most common in mathematical theory. However, with the advent of information technology, the binary system has become no less widespread, since it is the main way of representing information in computer memory.
Instructions
Conversion from decimal to binary is implemented for both integers and fractions. The translation of an integer decimal number is carried out by sequentially dividing it by 2. In this case, the number of iterations (actions) increases until the quotient becomes zero, and the final binary number is written as the resulting residues from right to left.
For example, the transformation of the number 19 looks like this: 19/2 = 18/2 + 1 = 9, the remainder is 1, we write 1;9/2 = 8/2 + 1 = 4, the remainder is 1, we write 1;4/ 2 = 2, there is no remainder, we write 0;2/2 = 1, there is no remainder, we write 0;1/2 = 0 + 1, the remainder is 1, we write 1. So, after the method of sequential division to the number 19 we got binary number 10011.
The calculator allows you to convert whole and fractional numbers from one number system to another. The base of the number system cannot be less than 2 and more than 36 (10 digits and 26 Latin letters after all). The length of numbers must not exceed 30 characters. To enter fractional numbers, use the symbol. or, . To convert a number from one system to another, enter the original number in the first field, the base of the original number system in the second, and the base of the number system to which you want to convert the number in the third field, then click the "Get Record" button.
Original number written in 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 -th number system.
I want to get a number written in 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 -th number system.
Get entry
Translations completed: 1237177
Number systems
Number systems are divided into two types: positional And not positional. We use the Arabic system, it is positional, but there is also the Roman system - it is not positional. In positional systems, the position of a digit in a number uniquely determines the value of that number. This is easy to understand by looking at some number as an example.
Example 1. Let's take the number 5921 in the decimal number system. Let's number the number from right to left starting from zero:
The number 5921 can be written in the following form: 5921 = 5000+900+20+1 = 5·10 3 +9·10 2 +2·10 1 +1·10 0 . The number 10 is a characteristic that defines the number system. The values of the position of a given number are taken as powers.
Example 2. Consider the real decimal number 1234.567. Let's number it starting from the zero position of the number from the decimal point to the left and right:
The number 1234.567 can be written in the following form: 1234.567 = 1000+200+30+4+0.5+0.06+0.007 = 1·10 3 +2·10 2 +3·10 1 +4·10 0 +5·10 -1 + 6·10 -2 +7·10 -3 .
Converting numbers from one number system to another
The simplest way to convert a number from one number system to another is to first convert the number to the decimal number system, and then the resulting result to the required number system.
Converting numbers from any number system to the decimal number system
To convert a number from any number system to decimal, it is enough to number its digits, starting with zero (the digit to the left of the decimal point) similarly to examples 1 or 2. Let's find the sum of the products of the digits of the number by the base of the number system to the power of the position of this digit:
1.
Convert the number 1001101.1101 2 to the decimal number system.
Solution: 10011.1101 2 = 1·2 4 +0·2 3 +0·2 2 +1·2 1 +1·2 0 +1·2 -1 +1·2 -2 +0·2 -3 +1·2 - 4 = 16+2+1+0.5+0.25+0.0625 = 19.8125 10
Answer: 10011.1101 2 = 19.8125 10
2.
Convert the number E8F.2D 16 to the decimal number system.
Solution: E8F.2D 16 = 14·16 2 +8·16 1 +15·16 0 +2·16 -1 +13·16 -2 = 3584+128+15+0.125+0.05078125 = 3727.17578125 10
Answer: E8F.2D 16 = 3727.17578125 10
Converting numbers from the decimal number system to another number system
To convert numbers from the decimal number system to another number system, the integer and fractional parts of the number must be converted separately.
Converting an integer part of a number from a decimal number system to another number system
An integer part is converted from a decimal number system to another number system by sequentially dividing the integer part of a number by the base of the number system until a whole remainder is obtained that is less than the base of the number system. The result of the translation will be a record of the remainder, starting with the last one.
3.
Convert the number 273 10 to the octal number system.
Solution: 273 / 8 = 34 and remainder 1. 34 / 8 = 4 and remainder 2. 4 is less than 8, so the calculation is complete. The record from the balances will look like this: 421
Examination: 4·8 2 +2·8 1 +1·8 0 = 256+16+1 = 273 = 273, the result is the same. This means the translation was done correctly.
Answer: 273 10 = 421 8
Let's consider the translation of regular decimal fractions into various number systems.
Converting the fractional part of a number from the decimal number system to another number system
Recall that a proper decimal fraction is called real number with zero integer part. To convert such a number to a number system with base N, you need to sequentially multiply the number by N until the fractional part goes to zero or the required number of digits is obtained. If, during multiplication, a number with an integer part other than zero is obtained, then the integer part is not taken into account further, since it is sequentially entered into the result.
4.
Convert the number 0.125 10 to the binary number system.
Solution: 0.125·2 = 0.25 (0 is the integer part, which will become the first digit of the result), 0.25·2 = 0.5 (0 is the second digit of the result), 0.5·2 = 1.0 (1 is the third digit of the result, and since the fractional part is zero , then the translation is completed).
Answer: 0.125 10 = 0.001 2
The positional number system first appeared in ancient Babylon. In India the system works as
positional decimal numbering using zero, the Indians have this number system
the Arab nation borrowed, and the Europeans, in turn, took from them. In Europe this system became
call it Arabic.
Positional system - the meaning of all digits depends on the position (digit) of a given digit in a number.
Examples, the standard 10th number system is a positional system. Let's say the number 453 is given.
The number 4 denotes hundreds and corresponds to the number 400, 5 - the number of tens and corresponds to the value 50,
and 3 - units and the value 3. It is easy to notice that as the digit increases, the value increases.
Thus, we write the given number as the sum 400+50+3=453.
Binary number system.
There are only 2 digits here - 0 and 1. Base of the binary system- number 2.
The number located at the very edge to the right indicates the number of units, the second number indicates
In all digits, only one digit is possible - either zero or one.
Using the binary number system, it is possible to encode any natural number by representing
This number is a sequence of zeros and ones.
Example: 10112 = 1*2 3 + 0*2*2+1*2 1 +1*2 0 =1*8 + 1*2+1=1110
The binary number system, like the decimal number system, is often used in computing
technology. The computer stores text and numbers in its memory in binary code and converts it programmatically
into the image on the screen.
Adding, subtracting and multiplying binary numbers.
Addition table in binary number system:
|
10 (transfer to senior rank) |
Subtraction table in binary number system:
|
(loan from senior category) 1 |
Example of column addition (14 10 + 5 10 = 19 10 or 1110 2 + 101 2 = 10011 2):
| + | 1 | 1 | 1 | 0 | |
| 1 | 0 | 1 | |||
| 1 | 0 | 0 | 1 | 1 |
Multiplication table in binary number system:
Example of column multiplication (14 10 * 5 10 = 70 10 or 1110 2 * 101 2 = 1000110 2):
| * | 1 | 1 | 1 | 0 | |||
| 1 | 0 | 1 | |||||
| + | 1 | 1 | 1 | 0 | |||
| 1 | 1 | 1 | 0 | ||||
| = | 1 | 0 | 0 | 0 | 1 | 1 | 0 |
Number conversion in the binary number system.
To convert from binary to decimal use the following table of exponents
bases 2:
Starting with the digit one, each digit is multiplied by 2. The dot after 1 is called binary point.
Convert binary numbers to decimal.
Let there be a binary number 110001 2. To convert to decimal we write it as a sum by
ranks as follows:
1 * 2 5 + 1 * 2 4 + 0 * 2 3 + 0 * 2 2 + 0 * 2 1 + 1 * 2 0 = 49
A little different:
1 * 32 + 1 * 16 + 0 * 8 + 0 * 4 + 0 * 2 + 1 * 1 = 49
It's also good to write the calculation as a table:
We move from right to left. Under all binary units we write its equivalent in the line below.
Convert fractional binary numbers to decimal numbers.
Exercise: convert the number 1011010, 101 2 to the decimal system.
We write the given number in this form:
1*2 6 +0*2 5 +1*2 4 +1*2 3 +0 *2 2 + 1 * 2 1 + 0 * 2 0 + 1 * 2 -1 + 0 * 2 -2 + 1 * 2 -3 = 90,625
Another recording option:
1*64+0*32+1*16+1*8+0*4+1*2+0*1+1*0,5+0*0,25+1*0,125 = 90,625
Or in table form:
|
0.25 |
0.125 |
||||||||
|
0.125 |
Convert decimal numbers to binary.
Suppose you need to convert the number 19 to binary. We can do it this way:
19 /2 = 9 with the remainder 1
9 /2 = 4 with remainder 1
4 /2 = 2 without a trace 0
2 /2 = 1 without a trace 0
1 /2 = 0 with the remainder 1
That is, each quotient is divided by 2 and the remainder is written to the end of the binary notation. Division
continues until there is no zero in the quotient. We write the result from right to left. Those. lower
number (1) will be the leftmost one and so on. So, we have the number 19 in binary notation: 10011.
Converting fractional decimal numbers to binary.
When a given number contains an integer part, it is converted separately from the fractional part. Translation
converting a fractional number from the decimal number system to the binary system occurs as follows:
- The fraction is multiplied by the base of the binary number system (2);
- In the resulting product, an entire part is isolated, which is taken as the leading one.
digit of a number in the binary number system;
- The algorithm terminates if the fractional part of the resulting product is zero or if
the required calculation accuracy has been achieved. Otherwise, calculations continue over
fractional part of the product.
Example: You need to convert the fractional decimal number 206.116 into a fractional binary number.
Translating the whole part, we get 206 10 =11001110 2. The fractional part of 0.116 is multiplied by base 2,
We put the whole parts of the product in the decimal places:
0,116 . 2 = 0,232
0,232 . 2 = 0,464
0,464 . 2 = 0,928
0,928 . 2 = 1,856
0,856 . 2 = 1,712
0,712 . 2 = 1,424
0,424 . 2 = 0,848
0,848 . 2 = 1,696
0,696 . 2 = 1,392
0,392 . 2 = 0,784
Result: 206,116 10 ≈ 11001110,0001110110 2
An algorithm for converting numbers from one number system to another.
1. From the decimal number system:
- divide the number by the base of the translated number system;
- find the remainder when dividing the integer part of a number;
- write down all remainders from division in reverse order;
2. From the binary number system:
- to convert to the decimal number system, we find the sum of the products of base 2 by
appropriate degree of discharge;
Those taking the Unified State Exam and more...
It is strange that in computer science lessons in schools they usually show students the most complex and inconvenient way to convert numbers from one system to another. This method consists of sequentially dividing the original number by the base and collecting the remainders from the division in reverse order.
For example, you need to convert the number 810 10 to binary:
We write the result in reverse order from bottom to top. It turns out 81010 = 11001010102
If you need to convert fairly large numbers into the binary system, then the division ladder takes on the size of a multi-story building. And how can you collect all the ones and zeros and not miss a single one?
The Unified State Exam program in computer science includes several tasks related to converting numbers from one system to another. Typically, this is a conversion between octal and hexadecimal systems and binary. These are sections A1, B11. But there are also problems with other number systems, such as in section B7.
To begin with, let us recall two tables that would be good to know by heart for those who choose computer science as their future profession.
Table of powers of number 2:
| 2 1 | 2 2 | 2 3 | 2 4 | 2 5 | 2 6 | 2 7 | 2 8 | 2 9 | 2 10 |
| 2 | 4 | 8 | 16 | 32 | 64 | 128 | 256 | 512 | 1024 |
It is easily obtained by multiplying the previous number by 2. So, if you do not remember all of these numbers, the rest are not difficult to obtain in your mind from those that you remember.
Table of binary numbers from 0 to 15 with hexadecimal representation:
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
| 0000 | 0001 | 0010 | 0011 | 0100 | 0101 | 0110 | 0111 | 1000 | 1001 | 1010 | 1011 | 1100 | 1101 | 1110 | 1111 |
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E | F |
The missing values are also easy to calculate by adding 1 to the known values.
Integer conversion
So, let's start by converting directly to the binary system. Let's take the same number 810 10. We need to decompose this number into terms equal to powers of two.
- We are looking for the power of two closest to 810 and not exceeding it. This is 2 9 = 512.
- Subtract 512 from 810, we get 298.
- Repeat steps 1 and 2 until there are no 1s or 0s left.
- We got it like this: 810 = 512 + 256 + 32 + 8 + 2 = 2 9 + 2 8 + 2 5 + 2 3 + 2 1.
Method 1: Arrange 1 according to the ranks of the indicators of the terms. In our example, these are 9, 8, 5, 3 and 1. The remaining places will contain zeros. So, we got the binary representation of the number 810 10 = 1100101010 2. Units are placed in 9th, 8th, 5th, 3rd and 1st places, counting from right to left from zero.
Method 2: Let's write the terms as powers of two under each other, starting with the largest.
810 =
Now let's add these steps together, like folding a fan: 1100101010.
That's all. At the same time, the problem “how many units are in the binary representation of the number 810?” is also simply solved.
The answer is as many as there are terms (powers of two) in this representation. 810 has 5 of them.
Now the example is simpler.
Let's convert the number 63 to the 5-ary number system. The closest power of 5 to 63 is 25 (square 5). A cube (125) will already be a lot. That is, 63 lies between the square of 5 and the cube. Then we will select the coefficient for 5 2. This is 2.
We get 63 10 = 50 + 13 = 50 + 10 + 3 = 2 * 5 2 + 2 * 5 + 3 = 223 5.
And, finally, very easy translations between 8 and hexadecimal systems. Since their base is a power of two, the translation is done automatically, simply by replacing the numbers with their binary representation. For the octal system, each digit is replaced by three binary digits, and for the hexadecimal system, four. In this case, all leading zeros are required, except for the most significant digit.
Let's convert the number 547 8 to binary.
| 547 8 = | 101 | 100 | 111 |
| 5 | 4 | 7 |
One more, for example 7D6A 16.
| 7D6A 16 = | (0)111 | 1101 | 0110 | 1010 |
| 7 | D | 6 | A |
Let's convert the number 7368 to the hexadecimal system. First, write the numbers in triplets, and then divide them into quadruples from the end: 736 8 = 111 011 110 = 1 1101 1110 = 1DE 16. Let's convert the number C25 16 to the octal system. First, we write the numbers in fours, and then divide them into threes from the end: C25 16 = 1100 0010 0101 = 110 000 100 101 = 6045 8. Now let's look at converting back to decimal. It is not difficult, the main thing is not to make mistakes in the calculations. We expand the number into a polynomial with powers of the base and coefficients for them. Then we multiply and add everything. E68 16 = 14 * 16 2 + 6 * 16 + 8 = 3688. 732 8 = 7 * 8 2 + 3*8 + 2 = 474 .
Converting negative numbers
Here you need to take into account that the number will be presented in two's complement code. To convert a number into additional code, you need to know the final size of the number, that is, what we want to fit it into - in a byte, in two bytes, in four. The most significant digit of a number means the sign. If there is 0, then the number is positive, if 1, then it is negative. On the left, the number is supplemented with a sign digit. We do not consider unsigned numbers; they are always positive, and the most significant bit in them is used as information.
To convert a negative number to binary code, you need to convert a positive number to binary, then change the zeros to ones and the ones to zeros. Then add 1 to the result.
So, let's convert the number -79 to the binary system. The number will take us one byte.
We convert 79 to the binary system, 79 = 1001111. We add zeros on the left to the size of the byte, 8 bits, we get 01001111. We change 1 to 0 and 0 to 1. We get 10110000. We add 1 to the result, we get the answer 10110001. Along the way, we answer the Unified State Exam question “how many units are in the binary representation of the number -79?” The answer is 4.
Adding 1 to the inverse of a number eliminates the difference between the representations +0 = 00000000 and -0 = 11111111. In two's complement code they will be written the same as 00000000.
Converting fractional numbers
Fractional numbers are converted in the reverse way of dividing whole numbers by the base, which we looked at at the very beginning. That is, using sequential multiplication by a new base with the collection of whole parts. The integer parts obtained during multiplication are collected, but do not participate in the following operations. Only fractions are multiplied. If the original number is greater than 1, then the integer and fractional parts are translated separately and then glued together.
Let's convert the number 0.6752 to the binary system.
| 0 | ,6752 |
| *2 | |
| 1 | ,3504 |
| *2 | |
| 0 | ,7008 |
| *2 | |
| 1 | ,4016 |
| *2 | |
| 0 | ,8032 |
| *2 | |
| 1 | ,6064 |
| *2 | |
| 1 | ,2128 |
The process can be continued for a long time until we get all the zeros in the fractional part or the required accuracy is achieved. Let's stop at the 6th sign for now.
It turns out 0.6752 = 0.101011.
If the number was 5.6752, then in binary it will be 101.101011.
