In the digital world, base conversion has always been a fundamental and important topic. From the binary, octal, decimal, and hexadecimal systems we learned as children, to bit operations in computer science, base conversions all play a vital role. Among them, decimal to binary conversions are useful in many situations, such as when understanding the representation of numbers inside a computer or when dealing with problems related to bit manipulation.
So, how do we use Python for decimal to binary conversion?
Method 1: Use the built-in functions of Python.
Python provides us with a very convenient built-in function that can implement this conversion directly. This function is called bin().
Example: Python
decimal_number = 10
binary_number = bin(decimal_number)
print(binary number) output: 0b1010
Here, the bin() function returns a string representing the binary number corresponding to a given decimal number. It is important to note that the output string starts with 0b, indicating that this is a binary number.
Method 2: Use mathematical methods
If you want to do this mathematically, you can use the remainder of division by 2. Specifically, it is to continuously divide a given decimal number by 2 and take the remainder until the quotient is 0. Each time the remainder is taken is one digit of the binary number.
Example: Python
def decimal_to_binary(decimal_number):
binary = ""
while decimal_number > 0:
binary = str(decimal_number % 2) +binary
decimal_number //= 2
return binary
decimal_number = 10
binary_number = decimal_to_binary(decimal_number)
print(binary number) output: 1010
Here, we define a function decimal to binary() to implement this conversion. This function gets the binary number by constantly dividing by 2 and taking the remainder. The last string returned is the binary representation.
Frequently Asked Questions
1.Why does binary only use 0 and 1?
Binary is a system of numbers with a base of 2. In binary, there are only two possible values for each bit: 0 or 1. This is different from the ten digits in the decimal system, which can be 0-9. The advantage of binary is that it is very suitable for interacting with logic gate circuits, so it is widely used in computer science.
2.Why does a computer use binary internally?
Computers are made up of logic gate circuits that have only two states: on (denoted as 1) or off (denoted as 0). As a result, binary is a very natural representation for computers. In addition, binary has only two numbers, simplifying the rules of operation and allowing the computer to perform calculations quickly.
3.How does binary do arithmetic?
In binary, addition and subtraction have some special rules. For example, there are only two possible outcomes for addition +1=0 and carry 1 (i.e. 1+1=10). There are similar rules for subtraction: for example, 1-1 = 0 and 1 (i.e. 1-1=1). These rules make the addition and subtraction of binary numbers very simple and fast.