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Bitwise & Number Systems

Decimal, binary, and hex; convert by hand; play with AND, OR, XOR, NOT, and shifts—then see where bitwise logic shows up in real programs.

binary & hex bitwise playground foundations

Bitwise Operations & Number Systems

the three number systems
systemdigits usedbaseexample: 42
decimal (human)0 1 2 3 4 5 6 7 8 91042
binary (computer)0 120b101010
hexadecimal (compact)0–9 A B C D E F160x2A
what each bit position is worth

Each position is a power of 2. Reading RIGHT to LEFT: 1, 2, 4, 8, 16, 32, 64, 128.

→ a byte = 8 bits. maximum value: 11111111 in binary = 255 in decimal.

drag to explore — any number 0–255
42
step-by-step: decimal to binary

The trick: keep dividing by 2. The remainders, read bottom-to-top, give you the binary number.

A first number
operator
B second number
where you will actually see bitwise operators in real code

even / odd check

Instead of n % 2 == 0, use (n & 1) == 0. Last bit of any even number is always 0. This is what low-level code does.

power of 2 check

n & (n-1) == 0 — a power of 2 has exactly one 1-bit. Subtracting 1 flips all bits below it. AND gives 0.

file permission flags (Linux)

chmod 755 is bitwise flags. Read=4, Write=2, Execute=1. OR them: 4|2|1 = 7 = full access.

RGB color masking

Extract red from 0xFF5733: (color >> 16) & 0xFF = 255. Used in every browser and image editor.

multiply / divide by 2 fast

n << 1 = n × 2. n >> 1 = n ÷ 2. Compilers use this internally for speed.

interview patterns (LeetCode)

Single number, counting bits, missing number, subset generation. All use XOR or AND. Once you see the pattern, these become straightforward.