* The logic circuits for digital systems are of two types. They are:
1.Combinational circuit
2.Sequential circuit
* A combinational circuit consists of logic whose
output is determined directly from the current input without using the previous
input.
* A sequential logic
circuit consists of logic gates whose output is dependent on current input and
previous input.
* A combinational circuit consists of input
variables,logic gates and output variables.
* The logic gates accept signals from the input and
generate signals to the output.
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*Here n input variables come from an external source
and m output variables go to external destination.
* There are different types of logic circuits
available.They are:
Adder:
1) It is
used to perform addition of 2 binary digits.
2)There
are four possible input combinations.They are: 00,01,10,11
3)When we
add two numbers the result will consists of sum and carry.
4)There are
two types of adders.They are:
1) Half Adder
2) Full Adder
1.Half Adder:
1) A
combinational circuit that perform the addition of 2 bits is known as half adder.
2) In this
input variables are known as augend and addend bits and the output variables
are known as sum and carry.
3)Here we
take 2 input variables as X and Y and the output as ‘S for sum’ and ‘C for
carry’.
4)We can
represent the input output combination for half adder in the following truth
table.
NOTE:-
- The Boolean function for sum is A'B+AB'
- The Boolean function for carry is AB
2.Full Adder:
1) This combinational circuit is used to perform sum
operations for 3 bits.
2) A full
adder consists of 3 inputs and 2 outputs.
3) The 3
input variables are represented by X, Y and Z and the 2 outputs are ‘S for sum’
and ‘C for carry’.
4) We can
represent the input output combination for full adder in the truth table as shown below.
5) We have to
simplify the Boolean function for sum and carry using k map.
6)The circuit diagram for full adder is as shown below
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