This online calculator is able to convert numbers from one number system to any other, showing a detailed course of solutions. And calculator designed for:
 Decimal to binary conversion,
 Binary to decimal conversion,
 Decimal to hexadecimal conversion,
 Decimal to binary conversion method,
 Floating point decimal to binary conversion method,
 Decimal to binary converter with steps,
 Decimal fraction to binary converter.
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Result: 

110101111000111010111100010110101100011000100000000000000000000.00000000000 Show how it happened 
You enter the number: 00100000000000000000000_{10} in Decimal number system and want to translate it into Binary.
Converting 1.0E+20_{10} in Binary system here so:
Whole part of a number is obtained by dividing on the basis new
7766279631452241920  2  
7766279631452241920  3883139815726120960  2  
0  3883139815726120960  1941569907863060480  2  
0  1941569907863060480  970784953931530240  2  
0  970784953931530240  485392476965765120  2  
0  485392476965765120  242696238482882560  2  
0  242696238482882560  121348119241441280  2  
0  121348119241441280  60674059620720640  2  
0  60674059620720640  30337029810360320  2  
0  30337029810360320  15168514905180160  2  
0  15168514905180160  7584257452590080  2  
0  7584257452590080  3792128726295040  2  
0  3792128726295040  1896064363147520  2  
0  1896064363147520  948032181573760  2  
0  948032181573760  474016090786880  2  
0  474016090786880  237008045393440  2  
0  237008045393440  118504022696720  2  
0  118504022696720  59252011348360  2  
0  59252011348360  29626005674180  2  
0  29626005674180  14813002837090  2  
0  14813002837090  7406501418545  2  
0  7406501418544  3703250709272  2  
1  3703250709272  1851625354636  2  
0  1851625354636  925812677318  2  
0  925812677318  462906338659  2  
0  462906338658  231453169329  2  
1  231453169328  115726584664  2  
1  115726584664  57863292332  2  
0  57863292332  28931646166  2  
0  28931646166  14465823083  2  
0  14465823082  7232911541  2  
1  7232911540  3616455770  2  
1  3616455770  1808227885  2  
0  1808227884  904113942  2  
1  904113942  452056971  2  
0  452056970  226028485  2  
1  226028484  113014242  2  
1  113014242  56507121  2  
0  56507120  28253560  2  
1  28253560  14126780  2  
0  14126780  7063390  2  
0  7063390  3531695  2  
0  3531694  1765847  2  
1  1765846  882923  2  
1  882922  441461  2  
1  441460  220730  2  
1  220730  110365  2  
0  110364  55182  2  
1  55182  27591  2  
0  27590  13795  2  
1  13794  6897  2  
1  6896  3448  2  
1  3448  1724  2  
0  1724  862  2  
0  862  431  2  
0  430  215  2  
1  214  107  2  
1  106  53  2  
1  52  26  2  
1  26  13  2  
0  12  6  2  
1  6  3  2  
0  2  1  
1  
Happened:7766279631452241920_{10} = 9223372036854775807_{2}
The fractional part of number is found by multiplying on the basis new
0  .0 
.  2 
Happened:0.0E+20_{10} = 0.00000000000_{2}
Add up together whole and fractional part here so:
9223372036854775807_{2} + 0.00000000000_{2} = 110101111000111010111100010110101100011000100000000000000000000.00000000000_{2}
Result of converting:
00100000000000000000000_{10} = 110101111000111010111100010110101100011000100000000000000000000.00000000000_{2}
 Type the numbers that need to be translated.
 Specify its numbering system.
 Specify in what number system translate.
 Click “Translate”.
 Click “Show progress of Solutions” For a detailed travel solutions.
Currency translation of numbers has one input field. In this field you must enter the number you want to translate.
After that, you definitely need to specify in what notation you entered it. “His number system” To this end, under the input field is a graph.
If you did not find your system, select “other” and the count will be the input field. In this field you must enter the base system by a single number without any spaces.
Next, you must choose the number you want to translate this into some system. If you did not find again the desired system then insert it in the “other”.
After click on “TRANSLATE” and the result will appear in the box. If you wish to receive a detailed course of solutions, please click on the appropriate link.
Numbers` transfer in different numeral systems
Numeral system is a collection of symbols (digits) and the rules of their use for numbers representation. There are two types of numeral systems. Non positional system – some letters are used as digits. Positional system – the quantitative value of the numbers depends on its place in the entry number. The position of figure is called discharge. Rank number increases from right to left. The number of different digits (characters) used in the positional numeral system for representing (record) number, is called the base.
The homogeneous system – for each category of the set of allowed symbols (digits) is the same. As an example, we use the decimal system. If to write the number in the homogeneous of the 10th system, it is possible to use in each discharge only one digit in the range of 0 – 9, thus, allowed number of 450 (grade 1^{st} – 0, 2^{nd} – 5, 3^{rd} – 4), and 4F5 – not, as the letter F is not included in a set of digits from 0 to 9.
Why should numbers be transferred from one system to another?
In the exercise of tasks on the computer introduction of the initial data and output the results of the calculations are usually performed by the user in the usual decimal notation for it. However, considering that the vast majority of computers use a binary numeral system, it appears the need to transfer numbers from one numeral system to another. Transfer of numbers from qone to decimal directly comes from the polynomial expression of a particular number.
The essence of this transfer is a sequential decimal number and its particular division to the radix`s value of the system q. The division is done until the next quotient is not less than the base q. The calculated residue on the last step is the oldest (first) digit of transferred number. The result of such transfer of the number in the qone numeral system is a record of the last quotient and all the residues in the reverse order.
Decimal numeral system
The decimal numeral system is the alphabet of digits, which consists of ten wellknown numbers, and a base of 10. Digit`s position in number is called discharge. Rank of number increases from right to left, from the junior to the senior ranks. In the decimal system the figure in the extreme right position (rank) represents the number of units; the shifted figures by one position to the left – the number of tens, still left – hundreds, thousands, and then so on. Accordingly, we have the category of units, tens rank, and so on.
Can be used the set of positional numeral systems, where the base is equal to or greater than 2. To convert numbers from the decimal to binary numeral system, use the socalled “replacement algorithm” consisting of the following sequences:
 Divide the decimal number A by 2. The quotient Q is remembered for the next step, and the remainder is written as the least significant bit of a binary number.
 If the quotient Q is not equal to 0, take it for a new dividend and repeat the procedure described in step 1. Each new remainder (0 or 1) is written in bits of the binary number in the direction from the LSB (least significant bit) to the eldest.
 The algorithm continues until get a private Q = 0, and the remainder a = 1 resulting from steps 1 and 2.
Binary numeral system
The binary numeral system is now used in virtually all digital devices. Computers, controllers, and other computing devices make calculations precisely in binary. Digital devices of audio recording and playing back, photo and video store and process the signals in binary notation. The transmission of information via digital communication channels uses a model of the binary system. The system is so named because her radix is two (2) or in a binary system 102 – this means that only two digits “0” and “1” are used for number image.
Deuce written down at bottom right from the number, hereinafter will be denote the radix. For the decimal system the radix is usually not indicated. To convert the binary number into a decimal, that number must be written as the radixes` sum of powers` product of the binary system to the corresponding figures in the ranks of the binary number.
Hexadecimal numeral system
The hexadecimal numeral system is the most popular means of recording compact binary digits. It is widely used in the design and development of digital technology. As the name implies, this system`s radix is number 16 or 1016 in the hexadecimal notation. So there was no mess, when writing numbers in positional number systems different from the decimal, to the right at the bottom from the main entry numbers the radix must be specified.
The first ten numbers are taken from the decimal system (0, 1, …, 8, 9) and has six letters (a, b, c, d, e, and f) added. In the hexadecimal number 3f7c2 letters “f” and “c” are hex digits. In the end of the hexadecimal number can be accepted the letter h. Thus it is possible to distinguish the hexadecimal numbers from other numbering systems.
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