Analysis and Design of Combinational and Sequential circuits

Logic circuits can be combinational or sequential. A combinational circuit consists of logic gates whose outputs at any time are determined from only the present combination of inputs. The operation of combinational circuits can be specified logically by a set of Boolean functions.

Sequential circuits contain storage elements in addition to logic gates. The outputs of sequential circuits are a function of the inputs and the state of the storage elements.

As the state of the storage elements is a function of previous inputs, the output of a sequential circuit depend not only on present values of inputs, but also on past inputs. The circuit behavior must be specified by a time sequence of inputs and internal states.

Combinational Circuits

A combinational circuit consists of an interconnection of logic gates. Combinational circuits react to the values at their inputs and produce the value of the output signal, transforming binary in formation from the given input data to a required output data.

Design of Combinational Circuits

To design the combinational circuits, the procedure involves the following steps:

• Find the required number of inputs and outputs and assign a symbol to each.
• Derive the truth table according to given specifications and function.
• Using the truth table, obtain simplified Boolean functions for each output as a function of the input variables.
• Draw the logic circuit diagram.

To obtain the output Boolean functions from a logic diagram, we do:

• Label all gate outputs with unique symbols.
• Find the Boolean functions for these gates.

To obtain the truth table directly from the logic diagram, steps are below:

• Determine the number of input variables in the circuit.
• Draw the table for these inputs. There are 2ⁿ combinations for the n input variables (0 to (2ⁿ - 1)).
• Label the outputs with unique symbols for gates in the circuit.
• Obtain the outputs of these gates in the table.

Example

Let's take an example of 3 Line to 8 Line Decoder:

• Inputs (3): A, B, C (binary input, say A is MSB)
• Outputs (8): Y₀ to Y₇ (only one is high at a time)

Truth Table:

• Y₀ = A̅B̅C̅
• Y₁ = A̅B̅C
• Y₂ = A̅BC̅
• Y₃ = A̅BC
• Y₄ = AB̅C̅
• Y₅ = AB̅C
• Y₆ = ABC̅
• Y₇ = ABC

Drawback of Combinational Circuits

If you need to design a system that stores and uses previous input and output, then we can not use a combinational circuit because it doesn't have capability to store any state or depend clock or and time. For these properties you can use Sequential circuits.

Sequential Circuits

Sequential circuits are logic circuits with memory. The output depends on current inputs and the past (i.e., previous state). They are digital circuits that store and use previous state information to determine their next state. They are commonly used in digital systems to implement state machines, timers, counters, and memory elements and are essential components in digital systems design

Types of Sequential Circuits:

• Synchronous: All flip-flops triggered by a common clock.
• Asynchronous: Flip-flops triggered independently.

Steps involved in designing sequential circuits

• Construct the truth table of the combinational network to determine the output and the input to the flip-flops.
• Use the characteristic table of the flip-flops to determine the next states.

Example

JA=B
KA=Bx'
JB=x'
KB=A' x +A x'

Step 1: Construct the truth table of the combinational network.

Step 2: Find A(t+1) and B(t+1), with the help of a characteristic table.

The characteristic table of a JK flip-flop,

Step 3: Final Table.

Drawbacks of Sequential Circuits

• Complexity Increases with States.
• Requires Synchronization with the clock.
• Flip-flops (memory elements) are required, which adds to hardware cost and power consumption.