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Circuit complexity measures the resources of Boolean circuits computing a Boolean function. Circuit size counts logic gates or wires under a declared convention; circuit depth measures the longest dependency chain. The allowed logic gates and their fan-in are part of the model.

For the conjunction of $n$ Boolean variables, a chain of two-input AND gates uses $n-1$ logic gates and depth $n-1$. A balanced binary tree still uses $n-1$ logic gates but reduces depth to $\lceil {\log }_{2}n\rceil$. A depth-$d$ Boolean circuit of fan-in at most two can depend on at most $2^d$ inputs, so that depth is optimal for this function. An unbounded-fan-in AND gate would compute it in one layer, showing why the logic gate convention matters.

A circuit family supplies one Boolean circuit per input length. uniform circuit families impose an effective construction rule; an unrestricted nonuniform family can choose separate Boolean circuits independently. Lower bounds therefore need both the Boolean circuit model and the uniformity convention.

A uniform circuit family $(C_n)$ has one effective rule generating its circuits rather than an independently supplied design at every input length. The precise resource limit on this rule is part of the definition. In logspace uniformity, a Turing machine given $1^n$ outputs a description of $C_n$ using $O(\log n)$ work space; its output tape is not counted as work space.

A family of balanced AND gate trees is uniform: a procedure can enumerate gates and their connections from the input length. In contrast, a nonuniform family can choose the constant output at length $n$ using membership of $n$ in an undecidable set. Those constant circuits are individually tiny, but no algorithm can generate the whole family. Uniformity therefore distinguishes small circuits that can be constructed effectively from arbitrary advice hidden in their choice. Stronger local-access conventions are also used when the circuit depth is so small that the cost of generating a complete description would obscure the intended complexity bound.