Design of combinatorial circuit and sequential circuit
A combinatorial circuit is a connected arrangement of logic gates with a set of input and output.
Fig: Block diagram of a combinatorial circuit
The design of combinatorial circuit starts from the verbal outline of the problem and ends in a logic circuit diagram.
Steps:
- the problem is stated
- the input and output variables are assigned letter symbols
- the truth table that defines the relationship between input and output is derived
- the simplified boolean function for each output are obtained
- the logic diagram is drawn
Half Adder
A combinatorial circuit that performs the arithmetic addition of two bits is called a half adder
i/p variables = augend and addend
o/p variables = sum and carry
It is necessary to specify two output variables because the sum of 1+1 is 10 which has two digits.
| x | y | c | s |
| 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 1 |
| 1 | 0 | 0 | 1 |
| 1 | 1 | 1 | 0 |
Truth Table
Full Adder
A combinatorial circuit that forms the arithmetic sum of three input. It has three input and two output. Two of the input variables represent the two significant bits to be added. The third input represents the carry from the previous lower significant prositions.
| Inputs | Outputs | |||
|---|---|---|---|---|
| A | B | Cin | Cout | S |
| 0 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 1 |
| 0 | 1 | 0 | 0 | 1 |
| 1 | 1 | 0 | 1 | 0 |
| 0 | 0 | 1 | 0 | 1 |
| 1 | 0 | 1 | 1 | 0 |
| 0 | 1 | 1 | 1 | 0 |
| 1 | 1 | 1 | 1 | 1 |
Sequential Circuit:
The storage elements employed in clocked sequential circuits are called flipflops. A flip-flop is a binary cell capable of storing one bit of information. It has two output, one for the normal value and one for the complement value of the bit stored in it.
A sequential circuit is an interconnection of flip-flop and gates. The gates by themselves constitute a combinational circuit, but when included with the flip-flops, the overall circuit is classified as a sequential circuit.
The behaviour of a sequential circuit is determined from the input output and the state of the flop-flip.