FULL ADDER CIRCUIT:
TRUTH TABLE
Full adder circuit has three inputs. It is a combination of two half adders. Full adder circuit has two outputs- sum and carry (circuitstoday.com/half_adder_and_full_adder). The Ex-OR gate gives the sum and the AND gate gives the carry of a half adder. The sum of a half adder is given as input along with the third input to another half adder comprising an Ex-OR gate and an AND gate. The output of the Ex-OR gate in the second half adder gives the sum. The carry of the first half adder and the second half adder are given as inputs to an OR gate whose output gives the carry for the three inputs.(hyperphysics.phy-astr.gsu.edu.hbase/electronic/fulladd.html)
De Morgan’s Laws:
There are two De Morgan’s laws. The laws help in simplifying Boolean expressions. The two laws are as given below:
1)
It states that, the negation of an OR gate (NOR gate)with two inputs – A and B is equivalent to an AND gate with inverted inputs- and.
The bar over them indicates NOT gate. The ‘+’ sign denotes OR and ‘.’ denotes AND. (allaboutcircuits.com/vol_4/chpt_8.htm)
EXAMPLE:
Let A be a high input and B be a low input. So A= 1 and B=0.
LHS:
Output of a NOR gate:
Putting values of A and B we get,
A+B=1
So,
RHS:
So, RHS=0.
Since LHS =RHS , the expression holds true.
Similarly, this expression can be verified for any possible value of A and B.
2)
It states that, the negation of an AND gate (NAND gate) with two inputs – A and B is equivalent to an OR gate with inverted inputs- and .
Where A and B are the inputs. The bar over them indicates NOT gate. The ‘+’ sign denotes OR and ‘.’ denotes AND.(bschshortnote.com/2013/09/de-morgans theorem-and-proof.html)
Example: Let A be a low input and B be a high input ie. A=0 and B=1
LHS:
So, LHS becomes 1
RHS:
1+0 = 1.
Hence the second theorem also holds good. Checking for other values of A and B
References:
- allaboutcircuits.com/vol_4/chpt_8.htm
- bschshortnote.com/2013/09/de-morgans theorem-and-proof.html
- circuitstoday.com/half_adder_and_full_adder
- hyperphysics.phy-astr.gsu.edu.hbase/electronic/fulladd.html
