Design Procedure

Design Procedure   AU: Dec.-07.08, May-08

Steps to design the combinational circuit

1. The problem definition.

2. The determination of number of available input variables and required output variables.

3. Assigning letter symbols to input and output variables.

4. The derivation of truth table indicating the relationships between input and output variables.

5. Obtain simplified Boolean expression for each output.

6. Obtain the logic diagram.

Examples for Understanding

Example 1.11.1 A majority gate is a digital circuit whose output is equal to 1 if the majority of inputs are 1's. The output is 0 otherwise. Using a truth table, find the Boolean function implemented by a 3-input gates. Simplify the function and implement with gates.   AU: Dec.-07, Marks 8

Solution :

Step 1: Derive the truth table for given statement.

Given problem specifies that there are three input variables and one output variable. We assign A, B and C letter symbols to three input variables and assign Y letter symbol to one output variable. The relationship between input variables and output variable can be tabulated as shown in truth Table 1.11.1.

Step 2: Obtain simplified Boolean expression. Now we obtain the simplified Boolean expression for output variable Y using K-map simplification.

Y = AC+ BC + AB

Step 3: Draw logic diagram.

In this chapter we are going to study various combinational circuits using above illustrated design method.

Implementation with 3-input gates

Example 1.11.2 Design a circuit that has one control line C and three data lines . When the control line is high, the circuit is to detect when one of the data lines has a 1 on it. No more than one data line will ever have a 1 on it. When the control line is low, the circuit will output a 0, regardless of what is on the data lines.

Solution: The truth table for the given problem is as shown below.

Examples for Practice

Example 1.11.3 Design a combinational circuit that generates the 9's complement of a BCD

digit.

Example 1.11.4 Design a combinational logic circuit with 4 inputs A, B, C, D. The output Y goes HIGH if and only if A and C inputs go HIGH. Draw the Truth table. Minimize the Boolean function using K-map. Draw the circuit diagram.

Example 1.11.5 Design circuit to detect invalid BCD number and implement using NAND gate only.

Example 1.11.6 Design a combinational logic circuit with three input variables that will produce logic 1 output when more than one input variables are logic 0.

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Review Question

1. What are the design procedures of combinational circuit ?     AU May-08, Marks 4