How many logic gates are needed to build the 4-bit carry-lookahead adder

Each B cell requires 3 gates. Hence, 12 gates are needed for all four B cells.

The carries c₁, c₂, c₃, and c₄ produced by the carry-lookahead logic, require 2, 3, 4, and 5 gates, respectively. According to the four logic expressions,

c₁ = G₀ + P₀c₀

c₂ = G₁ + P₁G₀ + P₁P₀c₀

c₃ = G₂ + P₂G₁ + P₂P₁G₀ + P₂P₁P₀c₀

C₄ = G₃ + P₃G₂ + P₃P₂G₁ + P₃P₂P₁G₀ + P₃P₂P₁P₀c₀

The carry-lookahead logic also produces G₀‘ using 4 gates, and P₀‘ using 1 gate. Hence, 19 gates are needed to implement the carry-lookahead logic. The complete 4-bit adder requires 12 + 19 = 31 gates, with a maximum fan-in of 5.