Data Type 1. – Numbers

Numeric data types are fundamental in any programming language, serving as the building blocks for mathematical operations. Python, a versatile and powerful language, offers three primary numeric data types: integers, floats, and complex numbers. In this blog, we’ll explore these data types, understand their characteristics, and examine their ranges.

1. Integers

Integers represent whole numbers, both positive and negative, without a decimal point. In Python, integers are of type int.

Integer Representation

Internally, integers in Python are represented using a fixed number of bits. The actual number of bits may vary based on the platform (32-bit or 64-bit). You can use the bit_length() method to determine the number of bits required to represent an integer.

num = 42
print(f"Binary representation of {num}: {bin(num)}")
print(f"Number of bits required: {num.bit_length()}")

Binary representation of 42: 0b101010
Number of bits required: 6

Integer Ranges

The range of integers in Python is determined by the underlying platform. For a standard 32-bit Python build:

Maximum value: 2³¹ − 1 or 2,147,483,647
Minimum value: −2³¹ or -2,147,483,648

For 64-bit Python builds, the limits are significantly higher.

2. Floats

Floats represent real numbers, including those with a decimal point or in exponential form. They are of type float in Python.

Floating-Point Representation

Floating-point numbers in Python are represented using the IEEE 754 standard. This standard defines how the sign, exponent, and fraction parts are encoded to represent real numbers.

float_num = 3.14
print(f"Binary representation of {float_num}: {float.as_integer_ratio(float_num)}")

Binary representation of 3.14: (7070651414971679, 2251799813685248)

Precision and Limitations

Floating-point numbers have limited precision due to the finite number of bits available for storage. This can sometimes result in rounding errors, especially in complex mathematical computations.

result = 0.1 + 0.1 + 0.1 - 0.3
print("Result of 0.1 + 0.1 + 0.1 - 0.3:", result)  # Expecting 0.0, but might not be exact

Result of 0.1 + 0.1 + 0.1 - 0.3: 5.551115123125783e-17

3. Complex Numbers

Complex numbers have a real and an imaginary part. They are of type complex in Python.

Complex Number Representation

Complex numbers in Python are represented as a+bj, where a is the real part, b is the imaginary part, and j is the imaginary unit.

complex_num = 2 + 3j
print("Real part:", complex_num.real)
print("Imaginary part:", complex_num.imag)

Real part: 2.0
Imaginary part: 3.0

4. Numeric Operations

Python allows a wide range of operations on numeric data types, including arithmetic operations (addition, subtraction, multiplication, division), exponentiation, modulus, and more.

# Arithmetic operations
result = 10 + 5
print("Addition:", result)

result = 10 - 5
print("Subtraction:", result)

result = 10 * 5
print("Multiplication:", result)

result = 10 / 5
print("Division:", result)

# Exponentiation
result = 2 ** 3
print("Exponentiation:", result)

# Modulus (remainder of division)
result = 10 % 3
print("Modulus:", result)

Addition: 15
Subtraction: 5
Multiplication: 50
Division: 2.0
Exponentiation: 8
Modulus: 1

Conclusion

Understanding numeric data types and their operations is fundamental in Python. Integers, floats, and complex numbers each serve different purposes and have their unique characteristics. Being proficient in utilizing these data types and performing numeric operations is essential for any Python programmer. Happy coding!