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Address decoding selects the correct memory location from an n-bit address using decoders. 2D decoding (row/column) reduces complexity; partial and hierarchical decoding further optimize large memories.
You already know how decoders work: an n-input decoder activates exactly one of 2n output lines based on the binary input. You also know that memory is organized as an array of storage locations, each holding a fixed number of bits. Address decoding is the bridge between these two concepts — it is the mechanism that translates a binary address from the CPU into the activation of one specific memory cell (or row of cells) within a memory chip.
Consider a simple example: a memory chip with 1,024 locations needs a 10-bit address. A straightforward approach would use a single 10-to-1024 decoder, but that decoder would have 1,024 output lines — an impractical number of wires and gates. Two-dimensional (2D) decoding solves this by splitting the address into two halves. The upper 5 bits select one of 32 rows, and the lower 5 bits select one of 32 columns. Now you need only a 5-to-32 row decoder and a 5-to-32 column decoder — 64 output lines total instead of 1,024. The selected memory cell sits at the intersection of the activated row and column, just like finding a seat in a theater by row letter and seat number.
Real systems take this further with hierarchical decoding. A computer with 4 GB of RAM doesn't have a single monolithic chip — it has many smaller memory chips organized into banks and modules. The highest-order address bits select which chip or bank is active (using a chip-select signal driven by a decoder), while the remaining bits perform the row/column decoding within that chip. Partial decoding is a simpler but less precise technique where not all address bits are decoded — some bits are ignored, causing the same physical memory to appear at multiple addresses (called aliasing). This was common in early microcomputers where simplicity mattered more than full address space utilization, but modern systems use full decoding to avoid wasting address space.