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## What are Combinational Digital Circuits

*Written by Harpreet*

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Combinational digital circuits are circuits in the digital domain in which the value of the output only depends upon the present values of all the inputs. Unlike a sequential digital circuit, these circuits have no memory element present within them. A few examples of combination digital circuits are: - Half Adder, Full Adder, Multiplier, code converters, Decoders, and Encoders etc. Every combinational circuit has a logical functional equation which relates the output to all the inputs. Using this equation, any combination digital circuits can be synthesized by using the fundamental AND, OR and NOT gates to picture the equation. But this is not the most effective method of realizing a digital circuit.

The mantra in digital electronics is to ‘use as less of a hardware as possible’ for the realization of the logic function. This is because lesser hardware leads to lower power consumption, lesser cost, more compatibility and higher speed of operation. Therefore the logical functional equation describing a combinational circuit must be in its most simplified form for its optimum hardware synthesis.

There are many mathematical tools that are available for a digital circuit designer to reduce the aforementioned logical functions in to their simplest forms. Out of these, the two most prominent ones are:-

Using Boolean Algebra Using Mapping

Boolean algebra is simply the use of Boolean mathematics to reduce the logical functional equation while Mapping is a graphical method used for the same purpose. Out of these two, mapping is the most reliable as there are fewer chances of making an error. Also while in Boolean algebra, a further simplification possible might miss the eye of the designer; mapping guarantees to reduce the logical function in to its most simplified form. For these reasons, mapping is often preferred in combinational circuit design over Boolean algebra.

Most combinational circuits use the positive logic in which the level ‘O’ is represented by O Volts and level ‘1’ is represented by +5 Volts. But with the increase in the popularity of portable digital devices such as cell phones, voltage scaling down (i.e. representation of the ‘1’ level by a lower voltage level) is being done in the digital domain by making appreciable changes in the designs of the IC’s. This is because a lower voltage level leads to lesser power consumption and therefore results in a longer battery life for the device.