Question

Draw the black box diagram of a full adder (FA) showing the inputs and the outputs

Design a 1-bit full adder circuit

Write the truth table

Get the simplified function of the outputs using k-maps.

Draw the circuit

Answer 1

1 bit adder which implies

0 +0 = 0

0 + 1 = 1

1 + 0 = 1

1 + 1 = 1 and carry =1

Draw the truth table by considering all the possible combinations with the input carry

Now the output side we have sum and carry out

Now draw the k map using the output

In terms of and/or/not gates k map doesn't help since there are none of the usual patterns, so this would require four minterms to represent the 'on' condition. So we will go with expression of the sum that is S= A xor B xor Cin.

So to draw we will draw another form of the table see the image below.

Functional one that is, fix AB and place the function of Cin the corresponding box .

Here the xor pattern is more obvious, and gives the required results. For carry out draw the usual K map which gives Cout=AB+Cin(A+B)

However, since we already have A⊕B to compute S, we might note that since the CinAB entry is covered by AB the remaining two terms can be written as Cin(A⊕B), which gives Cout=AB+Cin(A⊕B), thus sharing a gate with S.

So construction of full adder circuit is easier with directly with the expression obtained from the truth table instead of going for K map which is bit tricky.