Design a 4-bit combinational incremental circuit using four full adder circuits.

A 4-bit incrementer adds 1 to a 4-bit number $A_3A_2A_1A_0$. We use four full adders in a ripple chain. The second input $B$ of every adder is tied to 0. The carry input of the first adder is tied to 1, and this 1 is what gets added.

 A3     A2     A1     A0
  |      |      |      |
[FA3]<-[FA2]<-[FA1]<-[FA0]<-- C0 = 1   (B inputs = 0)
  |      |      |      |
 S3     S2     S1     S0

The first adder gives $S_0 = \overline{A_0}$ and carry $A_0$, and the carry moves up the chain. The output is $A + 1$. The last carry shows that $A$ was $1111$.