What is dec2bin
dec2bin.py is a python script that convert a binary to decimal and decimal with detail explanation in the console. The method used for the conversion is scoped from The Art of Assembly detailed explanation of binary and decimal in Chapter One. The method might not be the best approach for the conversion but it is more easy to grasp and understand what is really going on. This does not cater for float point values.
How do i use it
You first need to download the dec2bin.py script from the repo or clone the complete repo here. To run the script from command line or use it in another project you need Python installed on your system.
Method implemented from TAOA
This is copied from TAOA word for word.
The binary system works just like decimal numbering system with two exceptions: binary only allow the digit 0 and 1 (rather than 0 - 9), and binary uses powers of two rather than powers of 10. Therefore, it is easy to convert a binary number to decimal.
Binary to Decimal
For each “1” in the binary string, add in 2**n where “n” is the zero-based position of the binary digit. For example, the binary value 11001010 represents:
1*2**7 + 1*2**6 + 0*2**5 + 0*2**4 + 1*2**3 + 0*2**2 + 1*2**1 + 0*2**0
128 + 64 + 8 + 2
202
Decimal to Binary
To convert decimal to binary is slightly more difficult. You must find those powers of two which when added together produce the decimal result. The easiest method is to work from the a large power of two down to 2**0. Consider the decimal value 1359
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2**10 = 1024, 2**11 = 2048. So 1024 is the largest power of two less than 1359. Subtract 1024 from 1359 and begin the binary value on the left with a “1” digit. Binary = “1”, Decimal result is 1359 - 1024 = 335.
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The next lower power of two (2**9 = 512) is greater than the result from above, so add a “0” to the end of the binary string. Binary = “10”, Decimal result is still 335.
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The next lower power of two is 256(2**8). Substract this from 335 and add a “1” digit to the end of the binary number. Binary = “101”, Decimal result is 79.
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128 (2**7) is greater than 79, so tack a “0” to the end of the binary string. Binary = “1010”, Decimal result remains 79.
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The next lower power of two (2**6 = 64) is less than 79, so subtract 64 and append “1” to the end of the binary string. Binary = “10101”, Decimal result is 15.
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15 is less than the next power of two (2**5 = 32) so simply add a “0” to the end of the binary string. Binary = “101010”, Decimal result is still 15.
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16 (2**4) is greater than the remainder so far, so append a “0” to the end of the binary string. Binary = “1010100”, Deciomal result is 15.
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2**3 (eight) is less than 15, so stick another “1” digit on the end of the binary string. Binary = “10101001”, Decimal result is 7.
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2**2 is less than seven, so subtract four from seven and append another one to the binary string. Binary = “101010011”, decimal result is 3.
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2**1 is less than three, so append a one to the end of the binary string and subtract two from the decimal value. Binary = “1010100111”, Decimal result is now 1.
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Finally, the decimal result is one, which is 2**0, so add a final “1” to the end of the binary string. The final binary is “10101001111”.
Where is the code?
Yes the project is open source and the codes are here https://github.com/quickutils/dec2bin. Do not hesitate to make a contribution to the project or open an issue.
Licence
The project is licenced under the MIT Licence, which means you can uses it for whatever without any objectections and whatever you use it for is upto you.