Carry Lookahead Summary

Carry-lookahead addition circuits with logarithmic depth and quadratic size. This makes them much faster for reasonably sized $n$ but they take considerably more space. In practice, the larger circuit size and increased difficulty in laying out the circuit discourages designers from using a full carry-lookahead adder. Instead, a hybrid approach is used. With ripple-carry adders, $n$ $1$-bit adders were combined to form an $n$-bit adder. Instead, $n/m$ $m$-bit adders could be combined to form an $n$-bit adder. For example, $4$ $4$-bit carry-lookahead adders could be combined to form a $16$-bit adder. This approach gives a tradeoff between size and speed. Such a circuit has size proportional to $n * m$ and depth proportional to $n * \frac{\lg m}{m}$.