The term "ripple-carry" says it all: the carry bits ripple up from one binary digit to the next.
Quite simplified, this is the principle: With your 3-bit adder, the final stable result will be output not earlier than after all 1-bit adders have propagated their result.
coz the gates are the same
Yes, that is correct, but your conclusion is not. If you determine the propagation delay of the complete 3-bit adder by adding all propagation delays of the gates in the critical path, you get the maximum propagation delay. This is roughly 3 times the propagation delay of a 1-bit adder.
However, values do not change for each combination of an old calculation and a new calculation. So the actual propagation delay of a new calculation depends on the old calculation.
In my explanation below I assumed 000 + 000 = 000 and 001 + 000 = 001, respectively, as the old calculation to demonstrate a short and a long propagation delay. \$t_{PD}\$ is the propagation delay of a 1-bit adder.
In the first case (100 + 011 = 111), all 1-bit adders output the result after \$1 \times t_{PD}\$, because they work in parallel and do not have to add any carry. So the complete result is stable after \$1 \times t_{PD}\$.
|
\$0 \times t_{PD}\$ |
\$1 \times t_{PD}\$ |
\$2 \times t_{PD}\$ |
\$3 \times t_{PD}\$ |
| adder \$2 ^ 0\$ |
0 (old value) |
1 |
1 |
1 |
| adder \$2 ^ 1\$ |
0 (old value) |
1 |
1 |
1 |
| adder \$2 ^ 2\$ |
0 (old value) |
1 |
1 |
1 |
In the second case (001 + 111 = 000) the result needs \$3 \times t_{PD}\$, because each 1-bit adder can output the result only after the adder "before" has produced its output.
|
\$0 \times t_{PD}\$ |
\$1 \times t_{PD}\$ |
\$2 \times t_{PD}\$ |
\$3 \times t_{PD}\$ |
| adder \$2 ^ 0\$ |
1 (old value) |
0 |
0 |
0 |
| adder \$2 ^ 1\$ |
0 (old value) |
1 note 1 |
0 note 2 |
0 |
| adder \$2 ^ 2\$ |
0 (old value) |
1 note 3 |
1 note 3 |
0 note 4 |
Note 1: adder \$2 ^ 0\$ did not yet output its carry.
Note 2: adder \$2 ^ 0\$ did output its carry.
Note 3: adder \$2 ^ 1\$ did not yet output its carry.
Note 4: adder \$2 ^ 1\$ did output its carry.
