4 bit adder circuit not working(ttl)
First of all, you don't say what doesn't work.  Do the LED's ever light up?  Under what conditions?

I checked all of the wiring, and it looks okay (with one exception, see below); this is assuming the switches are wired correctly as you didn't provide a datasheet for them.

The one wiring anomaly is that you have n input (C0) that is left unconnected; this is not a good idea with TTL (or any logic for that matter).  Tie it either to ground or to VCC, and then use the left half or right half for the Outputs section of the truth table in the datasheet.

It's better actually to connect inputs like C0 to VCC through a resistor, like 4.7K.  This goes for all the switch inputs also.  However your circuit should work as shown with them tied to VCC.

There are some breadboards where power and ground are interrupted at the midpoint, and you need to bridge across the two sections horizontally so you have VCC and ground on both sides.  If this is the case, there is usually a bigger separation between those sections than the others.