Sum out S0 and carry out Cout of the Full Adder 1 is valid only after the propagation delay of Full Adder 1. In the same way, Sum out S3 of the Full Adder 4 is valid only after the joint propagation delays of Full Adder 1 to Full Adder 4. In simple words, the final result of the ripple carry adder is valid only after the joint propogation delays of all full adder circuits inside it.

To understand the working of a ripple carry adder completely, you need to have a look at the full adder too. Full adder is a logic circuit that adds two input operand bits plus a Carry in bit and outputs a Carry out bit and a sum bit.. The Sum out  (Sout) of a full adder is the XOR of input operand bits A, B and the Carry in (Cin) bit.  Truth table and schematic of a 1 bit Full adder is shown below

There is a simple trick to find results of a full adder. Consider the second last row of the truth table, here the operands are 1, 1, 0 ie  (A, B, Cin). Add them together ie 1+1+0 = 10 . In binary system,  the number order is 0, 1, 10, 11……. and so the result of 1+1+0 is 10 just like we get 1+1+0 =2 in decimal system. 2 in the decimal system corresponds to 10 in the binary system. Swapping the result “10” will give S=0 and Cout = 1 and the second last row is justified. This can be applied to any row in the table.

A Full adder can be made by combining two half adder circuits together (a half adder is a circuit that adds two input bits and outputs a sum bit and a carry bit).

#### Full adder using NAND or NOR logic.

Alternatively the full adder can be made using NAND or NOR logic. These schemes are universally accepted and their circuit diagrams are shown below.

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• H Melton
March 15, 2012

I believe the full adder truth table image file is wrong in the last row.

Should not Cout and S both be TRUE when inputs A,B, Cin are all TRUE?

I’ve included the URL for the full adder truth table file

• jojo
March 18, 2012

Hello Melton 🙂

Thanks for notifying us. We corrected it 🙂

• mojo khandani haula
May 14, 2013

hahaha. sab haule hai 😛

• Rajendher
September 28, 2013

hi,
actually you have not understood the TT of Full adder,
when A=1, B=1,Cin=1 it implies sum is 3 and it’s binary form is 11.so,we will have to write S=1 and Cout=1
please go through some standard book like marris mano.