Data representation and basic types

Computers represent all data as binary (base 2). Understanding how numbers and text are encoded prevents subtle bugs in scientific computing.

Number systems

Conversion: $1101_2 = 1\!\cdot\!2^{3} + 1\!\cdot\!2^{2} + 0\!\cdot\!2^{1} + 1\!\cdot\!2^{0} = 13_{10}$.

Basic Python types

x = 42          # int   — exact integer
y = 3.14        # float — IEEE 754 double (≈15 decimal digits)
s = "physics"   # str   — text
b = True        # bool  — True / False

Floating-point caution — Not all decimals are exact in binary:

>>> 0.1 + 0.2
0.30000000000000004

For scientific work, compare floats with a tolerance: abs(a - b) < 1e-9.

Type conversion

n = int("42")      # str → int
x = float("3.14")  # str → float
s = str(99)        # int → str

Physics link: When a simulation gives unexpected results, check for integer division (5 // 2 = 2) vs float division (5 / 2 = 2.5). This is a classic source of off-by-one physics errors.

Common pitfall: Floats are not real numbers: 0.1 + 0.2 ≠ 0.3 exactly. Compare numerical results with a tolerance, never with ==, or your simulation will "fail" for reasons that are pure representation.