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Carry Generation, Carry Propagation, Carry Deletion
To calculate delay in a ripple carry, we need to understand, how carry from one stage is affecting the next stage. For that, we need to analyze the dependence of output carry to the input carry.
From the truth table of Full adder,
Carry Generation:
When $A=1$ & $B=1$,
Comparing $C_{in}$ and $C_{out}$,
- $C_{out}$ is independent of $C_{in}$
- Whatever $C_{in}$ be, $C_{out}$ will always be $1$
- Hence we can say, Carry gets generated when $A=1$ & $B=1$
Carry generation involves $1$ AND $+$ $1$ OR gate delay
This carry generation process involves path from inputs $A$ and $B$ to output $C_{out}. Hence carry generation = $A$ to $C_{out}$ or $B$ to $C_{out}$.
Carry Propagation:
When $A=0$ & $B=1$ (or)Â $A=0$ & $B=1$,
Comparing $C_{in}$ and $C_{out}$,
- $C_{out}$ depends on $C_{in}$
- $C_{out}\;=\;C_{in}$
- Hence we can say, Carry gets propagated from one stage to next when $A=0$ & $B=1$ (or)Â $A=1$ & $B=0$
Carry Deletion:
When $A=0$ & $B=1$ (or)Â $A=0$ & $B=1$,
Comparing $C_{in}$ and $C_{out}$,
- $C_{out}$ is independent of $C_{in}$
- Whatever $C_{in}$ be, $C_{out}$ will always be $0$
- Hence we can say, Carry gets killed or deleted when $A=0$ & $B=0$
Upon summarizing,