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Computer organization Notes-Combinational Circuits

Combinational Logic Circuits are made up from basic logic gates that are “combined” or connected together to produce more complicated switching circuits. Combinational circuit is a circuit in which we combine the different gates in the circuit, for example Half Adder, Full Adder, Half Subtractor, Full Subtractor, encoder, decoder, multiplexer and demultiplexer. Combinational logic circuits can be very simple or very complicated. Some of the characteristics of combinational circuits are following −
• The output of combinational circuit at any instant of time, depends only on the levels present at input terminals.
• The combinational circuit does not use any memory. The previous state of input does not have any effect on the present state of the circuit.
• A combinational circuit can have an n number of inputs and m number of outputs.
Any Combinational circuit consists of input variables, logic gates and output variables. The block diagram of combinational circuit can be drawn as follows.
n input Variables               m output variables

Here n input variables take their values from some external sources, similarly, m output variable pass their values to some external sources. For n input variables, there are maximum 2n possible combinations. Hence, in a combinational circuit, every output variable can be defined as a function of these input combinations that will be unique for every output variable. A combinational circuit can also be specified with m Boolean functions, one for each output variable. Each output function is expressed in terms of the n input variables. A combinational circuit transforms binary information from the given input data to the required output data. Combinational circuits are used in digital computers for generating binary control decisions and for providing digital components required for data processing.
The design of combinational circuits starts from the verbal outline of the problem and ends in a logic circuit diagram. The procedure involves the following steps:
1. The problem is stated.
2. The input and output variables are assigned letter symbols.
3. The truth table that defines the relationship between inputs and outputs is derived.
4. The simplified Boolean functions for each output are obtained.
5. The Logic diagram is drawn.
To demonstrate the design of combinational circuits, we present two examples of simple arithmetic circuits. These circuits serve as basic building blocks for the construction of more complicated arithmetic circuits.

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