The bitwise XOR is a binary operation in which we compare two binary numbers bit by bit and return the value "1" if the bits are not same, and 0 if they are the same. The XOR(exclusive OR) operation follows the below rules - A B A ⊕ B ... Read More

Python allows you to perform the basic mathematical operations like addition, subtraction, multiplication, and division on large numbers as Python's integers are arbitrary-precision, hence there is no limit on their size.You can divide large numbers as you would normally do. But this has a lot of precision issues as such operations cannot be guaranteed to be precise, as it might slow down the language.Usually, dividing large numbers results in a floating-point number, which cannot be precise since Python's float can only accurately be represented up to 15-17 decimal digits.To overcome this issue, we can perform division operation using division operator ... Read More

You can multiply large numbers in Python directly without worrying about speed. Python supports a "bignum" integer type which can work with arbitrarily large numbers. In Python 2.5+, this type is called long and is separate from the int type, but the interpreter will automatically use whichever is more appropriate. As long as you have version 2.5 or better, just perform standard math operations, and any number which exceeds the boundaries of 32-bit math will be automatically (and transparently) converted to a bignum. To multiply large numbers in Python, we can use the basic multiplication operator or use the fractions ... Read More

Catalan numbers are defined as a sequence of natural numbers that can be used to find the number of possibilities of various combinations. The below formula is used to calculate catalan number using the binomial coefficient ( denoted as (nk) and represents the number of ways to choose k items from n )- For example, if the input parameter n is given 6, the output would be 142, that is calculated using the above formula in the following way: C(6)=C(0)C(5) + C(1)C(4) + C(2)C(3) + C(3)C(2) + C(4)C(1) + C(5)C(0) Following are the two main methods used to calculate the ... Read More

You can perform arithmetic operations on large numbers in python directly without worrying about speed. Python supports a "bignum" integer type which can work with arbitrarily large numbers. In Python 2.5+, this type is called long and is separate from the int type, but the interpreter will automatically use whichever is more appropriate.As long as you have version 2.5 or better, just perform standard math operations and any number which exceeds the boundaries of 32-bit math will be automatically (and transparently) converted to a bignum.examplea = 182841384165841685416854134135 b = 135481653441354138548413384135 print(a - b)OutputThis will give the output −47359730724487546868440750000

You can format a floating number to a fixed width in Python using the format function on the string. examplenums = [0.555555555555, 1, 12.0542184, 5589.6654753] for x in nums:    print("{:10.4f}".format(x))OutputThis will give the output −0.5556 1.0000 12.0542 5589.6655ExampleUsing the same function, you can also format integers −nums = [5, 20, 500] for x in nums:    print("{:d}".format(x))OutputThis will give the output −5 20 500ExampleYou can use it to provide padding as well, by specifying the number before d:nums = [5, 20, 500] for x in nums:    print("{:4d}".format(x))OutputThis will give the output −5 20 500The https://pyformat.info/ website is a great ... Read More

If you have binary numbers as strings, you can convert them to ints first using int(str, base) by providing the base as 2. Then add the numbers like you'd normally do. Finally convert it back to a string using the bin function. For example,a = '001' b = '011' sm = int(a,2) + int(b,2) c = bin(sm) print(c)This will give the output:0b100

Python comes with an amazing standard math library that provides all trigonometric functions like sin, cos, etc. You can import that library and use these functions. Note that these functions expect angles in radians. For example,import math angle1 = math.radians(90) angle2 = math.radians(60) print(math.cos(angle1)) print(math.cos(angle2))This will give the output:6.123233995736766e-17 0.5The first value is very close to zero. Such errors come due to computation limits.

To check if a float value is a whole number, use the float.is_integer() method. For example,print((10.0).is_integer()) print((15.23).is_integer())This will give the outputTrue False

Objects of different types except numbers are ordered by their type names; objects of the same types that don’t support proper comparison are ordered by their address. When you order two strings or two numeric types the ordering is done in the expected way (lexicographic ordering for string, numeric ordering for integers).When you order a numeric and a non-numeric type, the numeric type comes first.If you have a number in a str object, you can simply convert it to a float or an int using their respective constructors. For example, i = 100 j = "12" int_j = int(j) print(int_j ... Read More