Converting from decimal to binary in python

Convert Decimal to Binary Python Programs

In this article, we will look at 5 different ways to convert decimal to binary in Python.

Decimal and Binary Numbers

Decimal numbers are the numbers we use in our day-to-day life. It is a base 10 number system. The decimal number system has 10 digits from 0 to 9.

Binary numbers are the numbers that are represented in base 2. The binary number system has 2 digits 0 and 1.

Any decimal number can be converted to a binary number. For example, 10 in decimal is 1010 in binary.

Decimal numbers can be represented in binary format.

(0)10 = (0)2 (1)10 = (1)2 (2)10 = (10)2 (5)10 = (111)2 (10)10 = (1010)2 (15)10 = (1111)2 (50)10 = (110010)2 (100)10 = (1100100)2

To convert a decimal number to binary, we need to divide the decimal number by 2 and write the remainder in reverse order.

1. Decimal to Binary Python using bin() function

The bin() function is built-in function in Python. It can be used to convert a decimal number to a binary number.

It takes a single argument as input and returns the binary equivalent of the input number. The input number can be of any base but the output is always in base 2.

n = 10 print(bin(n)) # Output: 0b1010 n = 20 print(bin(n)) # Output: 0b10100

2. Decimal to Binary Python by Division by 2 (using array)

In the last method, we used a built-in python function to convert decimal to binary. In this method, we will use a simple algorithm to convert decimal numbers to binary.

Algorithm

1. Take a variable bin (to store the binary number) and initialize it to 0.
2. Take an empty array (list in python) arr to store the binary digits.
3. Now execute a while loop until the number is greater than 0.
4. Inside the loop, append the remainder of the number divided by 2 to the array and divide the number by 2.
5. Now reverse the array because the binary digits we get are in reverse order.
6. Now iterate through the array and multiply the variable bin by 10 and add the array element to it.
7. Finally, return the variable bin .

def dectobin(n): bin = 0 arr = [] while n > 0: arr.append(n % 2) n //= 2 arr.reverse() for i in arr: bin = bin * 10 + i return bin n = int(input("Enter a decimal number: ")) print(dectobin(n))

Enter a decimal number: 25 Binary number: 11001

3. Decimal to Binary Python by Division by 2 (without using array)

In this method, we will use the same algorithm as in the previous method but we will not use an array to store the binary digits.

With a little modification, we can store the binary digits in a variable and return it.

Algorithm

1. Take a variable bin (to store the binary number) and initialize it to 0.
2. Take a variable i and initialize it to 1. This variable will be used to multiply the binary digits with the power of 10.
3. Now run a while loop until the number is greater than 0.
4. Inside the loop, add the remainder of the number divided by 2 to the variable bin and multiply it by the variable i .
5. Now divide the number by 2 and multiply the variable i by 10.
6. Finally, return the variable bin .

def dectobin(n): bin = 0 i = 1 while n > 0: bin = bin + (n % 2) * i n //= 2 i *= 10 return bin n = int(input("Enter a decimal number: ")) print(dectobin(n))

Enter a decimal number: 50 Binary number: 110010

4. Decimal to Binary Python using Recursion

Recursion is a method of solving a problem where the solution depends on solutions to smaller instances of the same problem.

We will call the same function recursively with the quotient of the number divided by 2 as the argument.

def dectobin(n): if n == 0: return 0 else: return n % 2 + 10 * dectobin(n // 2) n = int(input("Enter a decimal number: ")) print(dectobin(n))

Enter a decimal number: 100 Binary number: 1100100

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Convert Decimal to Binary in Python

Base ten digits, ranging from 0 to 9, are used in the decimal or «denary» binary counting system. It is the most widely used system of numbering. Every digit in this system has a place and a decimal point. On the other hand, the binary system employs integers in base two, ranging from 0 to 1. It is the most straightforward system because it has two digits: 0 and 1. As a result, it is common for experts in computer programming or other related engineering fields to need to transform decimal code to binary.

Introduction

Binary is one of the most important foundational aspects of Computers and other Digital Systems. As we humans use languages to understand and communicate with each other, Computers and other Digital Systems use Binary. It is a base-2 number system with only two numbers, 0 & 1 , corresponding to ON & OFF states that your computer can understand.

As normal humans have ten fingers to represent a simple number system called Decimal, computers have these ON & OFF states representing Binary. So to understand and interpret the Binary, we need some technique to convert binary code into decimal (human-readable) code and vice versa. Thus, this article will discuss how to convert Decimal to Binary and vice versa, in context with one of the computer programming languages, Python.

Understanding Decimal and Binary

Decimal System(Base-10) uses ten numbers ranging from 0 to 9 and then uses their combinations to form digits, with each digit being worth ten times more than the last digit (1, 10, 100, so-on) going from left to right.

• Here, 265 is a combination of numbers ranging from 0 to 9 to form each digit
• Each digit is ten times more than the last digit going from left to right 5 -> 5×100; 6 -> 6×101; 2 -> 2×102

Binary System(Base-2) is also similar. It is a combination of numbers 0 or 1, with each digit worth two times more than the last digit(1, 2, 4, so-on) going from left to right.

Decimal Digit Representation:

…	[0 to 9]	[0 to 9]	[0 to 9]	[0 to 9]	[0 to 9]
…	1 0 4 10^4 1 0 4	1 0 3 10^3 1 0 3	1 0 2 10^2 1 0 2	1 0 1 10^1 1 0 1	1 0 0 10^0 1 0 0
N t h N^	N t h digit	5 t h 5^	5 t h digit	4 t h 4^	4 t h digit	3 r d 3^ 3 r d digit	2 n d 2^ 2 n d digit	1 s t 1^ 1 s t digit

Binary Digit Representation:

…	[0 or 1]	[0 or 1]	[0 or 1]	[0 or 1]	[0 or 1]
…	2 4 2^4 2 4	2 3 2^3 2 3	2 2 2^2 2 2	2 1 2^1 2 1	2 0 2^0 2 0
N t h N^	N t h digit	5 t h 5^	5 t h digit	4 t h 4^	4 t h digit	3 r d 3^ 3 r d digit	2 n d 2^ 2 n d digit	1 s t 1^ 1 s t digit

Binary to Decimal Conversion in Python

We have already seen that the Binary System is a combination of [0 or 1], with each digit worth two times more than the last digit, so let’s see how this information will help us convert binary to decimal equivalent.

Consider a Binary Number 01011

( 0 1 0 1 1 ) 2 = ( 0 × 2 4 ) + ( 1 × 2 3 ) + ( 0 × 2 2 ) + ( 1 × 2 1 ) + ( 1 × 2 0 ) = ( 0 ) + ( 8 ) + ( 0 ) + ( 2 ) + ( 1 ) = ( 1 1 ) 1 0 (01011)^2 = (0×2^4) + (1×2^3) + (0×2^2) + (1×2^1) + (1×2^0) = (0)+(8)+(0)+(2)+(1) =(11)_ <10>( 0 1 0 1 1 ) 2 = ( 0 × 2 4 ) + ( 1 × 2 3 ) + ( 0 × 2 2 ) + ( 1 × 2 1 ) + ( 1 × 2 0 ) = ( 0 ) + ( 8 ) + ( 0 ) + ( 2 ) + ( 1 ) = ( 1 1 ) 1 0 ​

Therefore, the binary(base-2) ( 0 1 0 1 1 ) 2 (01011)_2 ( 0 1 0 1 1 ) 2 ​ is equivalent to ( 1 1 ) 1 0 (11)_ ( 1 1 ) 1 0 ​ Decimal(base-10) number.

Convert Binary to Decimal in Python

We will see how to convert binary to Decimal in Python using a built-in function.

Built-in Function in Python to convert Binary to Decimal:

In Python, we can use the int() function to convert a binary to its decimal value. The int() function takes 2 arguments, a value and the base of the number to be converted, which is 2 in the case of binary numbers

Decimal to Binary Conversion in Python

Let’s try to understand the Decimal to binary conversion. The easiest technique to convert the decimal numbers to their binary equivalent is the Division by 2 .

In Division by 2 technique, we continuously divide a decimal number by 2 and note the reminder till we get 1 as our input value. Then we read the noted reminders in reverse order to get the final binary value.

Let’s break the earlier statements to get more clarity. Assume we have a special function that divides the input number by 2 and gives the remainder as output. For Decimal to Binary, we call this special function multiple times till we get the 1 as the input value. Then, we finally print all the saved reminders to get the final binary(base-2) value.

Converting Decimal To Binary in Python

Now we will see how to code the Decimal to Binary in Python. We will first try to code the technique we learned using a custom recursive function call in Python.

1. Custom Recursive Function in Python to convert Decimal to Binary:

In this sample, we will write the special function(DecimalToBinary) to implement for obtaining quotients(input to next function call) and the remainder(output value), and then we will call it repeatedly till the input value is greater than and equal to 1

Apart from this, Python also provides a built-in function to convert Decimal to Binary.

2. Built-in Function in Python to convert Binary to Decimal:

In Python, we can simply use the bin() function to convert from a decimal value to its corresponding binary value. The bin() takes a value as its argument and returns a binary equivalent.

Note: bin() return binary value with the prefix 0b , so depending on the use-case, formatting should be done to remove 0b .

We can also convert Decimal to Binary in another way apart from using the built-in function from Python.

3. Without using Built-in Function in Python to convert Binary to Decimal:

Conclusion

1. Most Computers and Digital systems use binary because of their reliable storing of data.
2. The Decimal system (base-10) uses a combination of numbers from 0 to 9 to form digits, with each digit being worth ten times more than the last digit.
3. The Binary system (base-2) uses a combination of 0 or 1 to form digits, with each digit being worth two times more than the last digit.
4. Binary to Decimal conversion is each digit’s weighted sum (2i x ith-value) .
5. Binary to Decimal in Python can be performed using the built-in function int(, )
6. Decimal to Binary conversion is achieved using the Division By 2 technique.

Some of the ways to convert Decimal to Binary in Python are by using a custom recursive function, built-in functionbin() or using “”.format(int()).

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Convert decimal to binary in python [duplicate]

Is there any module or function in python I can use to convert a decimal number to its binary equivalent? I am able to convert binary to decimal using int(‘[binary_value]’,2), so any way to do the reverse without writing the code to do it myself?

Unlike the linked question «convert to binary string», I think this question is different. I came here looking to convert an integer to a corresponding binary array (or boolean array), and I think that would be a sensible answer.

8 Answers 8

all numbers are stored in binary. if you want a textual representation of a given number in binary, use bin(i)

@WaldoBronchart thats cool. Can you explain to me how does that work, having the leading zeros? Is that inbuilt, that you get the leading zeros with 0+8 or 0+16?

same for me with python 3.5.2 TypeError: non-empty format string passed to object.__format__ ahh — now i got it, what you meant: «`>>> «<0:b>«.format(47) —> ‘101111’

You also can determine amount of bits that it will be represented in this way:>>> «<:0>15b>».format(3) >>> ‘000000000000011’

def dec_to_bin(x): return int(bin(x)[2:]) 

-1 — don’t return an int. Also, dec_to_bin(-1) gives ValueError: invalid literal for int() with base 10: ‘b1’

Try bin(2) . You don’t get ’10’. You get ‘0b10’. Same possible pit with hex(2) (‘0x2’). So you want all but the first two characters. So you take a slice that starts after the first two characters.

@Wallace: because binary and decimal are a choice of how to show the number, not part of the number itself. dec_to_bin(0b101) == 101 , which is nonsense because none of operations you can apply to 101 have any relation to the original 5 — for instance, dec_to_bin(0b101) + 1 == 102 .

You can also use a function from the numpy module

from numpy import binary_repr 

which can also handle leading zeros:

Definition: binary_repr(num, width=None) Docstring: Return the binary representation of the input number as a string. This is equivalent to using base_repr with base 2, but about 25x faster. For negative numbers, if width is not given, a - sign is added to the front. If width is given, the two's complement of the number is returned, with respect to that width. 

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