Which 2-input gate consumes more dynamic power: an AND gate or an XOR gate, given equal...
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Which 2-input gate consumes more dynamic power: an AND gate or an XOR gate, given equal transition probabilities at their inputs?
Show answer & explanation
Dynamic power is proportional to the switching activity factor, load capacitance, and supply voltage squared. An XOR gate has a higher internal transistor count and a higher switching activity factor than an AND gate for the same input transition probabilities, so it consumes more dynamic power.
Step-by-step Derivation:
Dynamic power is given by P_dyn = α * C_L * V_DD^2 * f, where α is the switching activity factor. For a 2-input AND gate, the output is 1 only when both inputs are 1, so the probability of the output being 1 is 1/4. For a 2-input XOR gate, the output is 1 when the inputs are different, so the probability of the output being 1 is 1/2. The switching activity factor α = 2 * P(1) * P(0). For AND: α = 2 * (1/4) * (3/4) = 3/8. For XOR: α = 2 * (1/2) * (1/2) = 1/2. Since 1/2 > 3/8, the XOR gate has a higher switching activity factor. Additionally, an XOR gate requires more transistors (typically 6-10 transistors) than an AND gate (typically 6 transistors including the inverter), leading to higher internal capacitance. Therefore, the XOR gate consumes more dynamic power.