Adders
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 Generation stage acts like a wall. It won’t pass along the previous stage’s carry to next stage.
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 $A=0$ & $B=0$
Carry deletion stage acts like a wall. It won’t pass along the previous stage’s carry to next stage.
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 Propagation stage acts like a tunnel. It will pass along the previous stage’s carry to next stage.
Upon summarizing,
Wall and Tunnel:
- Carry Propagation stage will act like a tunnel. It will pass along the previous stage’s carry to next stage.
- Carry deletion and generation stage will act like a wall. It won’t pass along the previous stage’s carry to next stage.
Delay depends on the input applied:
Time taken by the adder to deliver correct output depends on the inputs applied.
When all inputs are zero $A=0000\;\;B=0000$:
- Each and every stage will act as a carry kill stage.
- No stage will generate any carry and no stage will depend on its previous stage’s carry.