How many unique combinations of 0's and 1's can be made with 5-binary-digit…

The Fundamental Principle of Counting states that when a task is completed through a sequence of independent choices — a first choice with n1 options, a second choice with n2 options, and so on through a k-th choice with nk options — the total number of distinct outcomes for the whole sequence equals the product n1 × n2 × ... × nk. Each binary digit (bit) independently takes exactly 2 possible values: 0 or 1.

1. A 5-binary-digit code has 5 independent bit positions, and each position can independently be filled with 2 values (0 or 1).

2. By the fundamental counting principle, the total count of distinct 5-bit codes is the product of 5 factors of 2: 2 × 2 × 2 × 2 × 2.

3. 2 × 2 × 2 × 2 × 2 = 25 = 32.

This matches the doubling pattern obtained by building up bit-by-bit: 1 bit gives 2 combinations (0, 1); 2 bits give 4 (00, 01, 10, 11); 3 bits give 8; 4 bits give 16; and 5 bits give 32 — each added bit doubles the previous count, confirming 25 = 32.