Combinational Logic

Combinational circuits are types of digital circuits that output a binary value, based on a set of input signals. These circuits are generally constructed using logic gates such as AND, OR, NOT, NAND, and NOR gates. They do not have any memory elements or feedback loops, meaning the output only depends on the current input conditions.

Combinational circuits are used for tasks that involve mathematical computations, such as adders and multipliers, as well as logic operations, such as reduction and comparison. They are widely used in digital systems and applications such as computers, calculators, and communication systems.

They are called so because they generate outputs based on the combination of their input values. This means that the output of a combinational circuit only depends on the current input values and not on the previous input values or the state of the circuit. The output is simply a combination of the input values, which is generated using logic gates such as AND, OR, NOT, NAND, and NOR gates. This is in contrast to sequential circuits, which have output values that depend not only on the current input values but also on the previous input values and the internal state of the circuit.

Characteristics

Some characteristics of combinational circuits include:

  • No feedback loop: Combinational circuits use logic gates to produce the output, and there are no feedback loops in these circuits. This means that the output of the circuit depends only on the current input values, and not on any previous input values or internal state of the circuit.
  • Fixed timing: The output of a combinational circuit is available instantly once the input values are applied. Combinational circuits have fixed and known timing delays, which does not change with the input values.
  • No memory: Combinational circuits do not have any memory elements, which means that the output of the circuit is not stored in any way. This makes the circuits ideal for performing mathematical computations and logical operations, but unsuitable for storing data.
  • Boolean algebra: Combinational circuits use Boolean algebra to perform operations. They use several basic Boolean algebraic operations like AND, OR, NOT etc., to create more complex functions.
  • Simple design: Combinational circuits are easier to design than sequential circuits, making them less prone to errors during design and less expensive to manufacture.

    • Example

    An example of a combinational circuit is an Adder circuit. An Adder circuit is a digital circuit used in computing to perform arithmetic operations such as addition of binary values. An adder circuit has two or more inputs, and the output is the sum of the inputs.

    The full adder circuit is a type of adder circuit that takes three inputs: two binary inputs (A and B) and a carry input (C-in). It generates two outputs: a sum output (S) and a carry output (C-out). The circuit combines the binary inputs with the carry input to produce the sum and carry outputs.

    The logic gates used in the full adder circuit include XOR, AND, and OR gates. The truth table of a full adder circuit shows the output values based on the input values. This combinational circuit is widely used in binary arithmetic and digital signal processing.

    Common Combinational Logic Circuits

    There are several combinational circuits that are frequently used in digital design. Some of the main combinational circuits are:

    • Adders: Adders are digital circuits that perform binary addition of two or more operands. Half-Adders, Full-Adders, ripple-carry adders, carry-lookahead adders, and carry-select adders are some examples of adders.
    • Multiplexers: A multiplexer is a digital circuit that selects one of several input signals and forwards the selected input to the output. Multiplexers are also known as data selectors, data selectors/multiplexers, or data selectors/demultiplexers.
    • Decoders: A decoder is a digital circuit that converts a binary/multilevel input into a set of output signals. Decoders are widely used in digital systems for address decoding, memory selection, etc.
    • Encoders: An encoder is a digital circuit that converts one or more input signals into a binary/multilevel output code. Encoders are used for data compression, data translations, and data encryption applications.
    • Comparators: A comparator is a digital circuit that compares two binary numbers and generates output signals indicating if the two inputs are equal or not. Comparators are used for testing and sorting data in digital systems.
    • Code converters: Code converters are digital circuits that convert one type of data representation into another. Some examples of code converters include BCD-to-binary and binary-to-BCD converters.
    • Priority encoders: Priority encoders are digital circuits that assign a priority to several input signals and generate an output code that represents the highest-priority active input signal.

    Click here for an example of a design using truth tables, k-maps and logic gates !