DIGITAL LOGIC : COMBINATIONAL CIRCUIT

A combinational circuit is a circuit  made up by combining logic gates such that the required logic at the output(s) depends only on the input logic present condition, both completely specified by either a truth table or by a Boolean expression.

Characteristics

(i) An output(s) remains constant, as long input conditions do not require change in output(s).

(ii) An output depends solely on the current input condition and not on any past input condition or past output condition.

(iii) A combinational circuit has no feedback of the output from a stage to the input of either that stage or any previous stage.

(iv) An output(s) at each stage appears after a delay in few tens or hundred ns depending upon the type or family of the gate used to implement the circuit.

Combinational circuit representation

1.  i). A block diagram for n inputs and m outputs.

    ii). A truth table of 2ⁿ rows

Example- Truth Table Four Rows for 2 inputs and 1 output

   Inputs                          Output

A1     A2                            F

 0        0                             1

 0        1                             0

 1        0                             0

 1        1                             0

2.  i). SOP terms (2ⁿ miniterms) for each output

    ii). POS terms (2ⁿ maxterms) for each output

   iii). Karnaugh map of n variables and 2ⁿ cells

FORMULATION OF A PROBLEM IN A COMBINATIONAL CIRCUIT

A). First step is to select the combinational circuit(s) in a logic network for which the problem of designing as per specifications is to be solved.

B). Criteria for whether a problem or its part is solvable by a combination circuit or not, is as follows:

     1). Criteria for whether a problem or its part is solvable.

        i). Check whether the required logic at the output(s) depends only on the input logic conditions, both completely specified by either a truth table or by a Boolean expression.

       ii). Check whether an output(s) remains same, as long present input condition does not require the change in the output(s).

      iii). Check whether an output depends solely on the current input condition and not on any past input condition or past output condition.

Specification of each output as a function of input conditions

1. Specify the number of inputs, n. The n is also the number of literals in a Boolean expression for an output.

2. Specify the number of outputs, m.

3. Specify the delays permitted at the outputs.

4. Specify the fan-ins permitted at the inputs.

5. Specify fan-outs permitted from the targets gates and building blocks.

6. Design a ‘truth table’ for n inputs and m outputs. Each output corresponds to each possible combination of input conditions.

7.Write a Boolean expression for the logic circuit for each output: The n is also the number of literals in a Boolean expression for output.

8. Specify as SOP or POS standard Format

Specification of gate characteristics

1. Propagation delays

2. Fan-ins permitted are specified in the problem

3. If a possible combination of the input condition is unspecified or is don’t care, specify it by ‘x’. [The Boolean expression for the output is an incomplete Boolean function.]

4. If a possible condition is high impedance output ‘tristate’, specify it by  ‘*’.

Summary

1. A combinational circuit — made up by combining logic gates such that:

i). Required logic at the output(s) depends only on the input logic present condition.

ii). Both (inputs and output) completely specified by a truth table or Boolean expression.

2. A combinational circuit — Problem Formulation means

i). Building block selection

ii). Defining Specifications