Address Space

Each address bit can take one of two values, 0 or 1, so n bits produce 2 × 2 × ... × 2 possible patterns, which equals 2^n. Each unique bit pattern can label one distinct memory location, so the total number of addressable locations is the number of possible addresses. This is why increasing the number of address bits doubles the address space each time you add one more bit.

Use this when calculating how many memory cells, bytes, or other locations a CPU or system can directly name with a given number of address bits. It is also useful when converting between address width and memory capacity in architecture, operating systems, and embedded systems.

• Using n instead of 2^n, which undercounts badly
• Forgetting that each added address bit doubles the number of locations
• Confusing addressable locations with total memory size without checking whether each location is a byte or a larger unit