# Whats the difference with Carry Look Ahead Generator & Block Carry Look Ahead Generaor

Whats the difference between this 2 CLAG (Carry Look Ahead Generator)

CLAG

Block CLAG

I mean, the way Carries of 1st 3 bits are the same and the last carry is actually $G*$? The difference is use of different gates and the additional $P*$ bit?

Equation of 1st image (I'll use 0 index. eg. $P_0 \text{ to } P_3, C_{-1} \text{ to } C_3$). Where $C_{-1}$ is carry into circuit

$C_3 = G_3 + P_3 \cdot G_2 + P_3 \cdot P_2 \cdot G_1 + P_3 \cdot P_2 \cdot P_1 \cdot G_0 + P_3 \cdot P_2 \cdot P_1 \cdot P_0 \cdot C_{-1}$

$C_2 = G_2 + P_2 \cdot G_1 + P_2 \cdot P_1 \cdot G_0 + P_2 \cdot P_1 \cdot P_0 \cdot C_{-1}$

$C_1 = G_1 + P_1 \cdot G_0 + P_1 \cdot P_0 \cdot C_{-1}$

$C_0 = G_0 + P_0 \cdot C_{-1}$

Equation for image 2 ("Block" CLAG)

$C_1 = (G_1' \cdot (P_1 \cdot G_0)' \cdot (P_1 \cdot P_0 \cdot C_{-1})')'$

$= G_1 + (P_1 \cdot G_0) + (P_1 \cdot P_0 \cdot C_{-1}) \rightarrow \textrm{ DeMorgans}$

So aren't they the same, with the addition of a $P*$ bit, or did I miss something?