Combinational Logic Circuit Design

Even though CAD tools are used to create combinational logic circuits in practice, it is important that a digital designer should learn how to generate a logic circuit from a specification. Understanding this process allows the designer to better use the CAD tools, and, if need be, to design critical logic sub-circuits by hand.

Design procedure

The design procedure for combinational logic circuits starts with the problem specification and comprises the following steps:

  1. Determine required number of inputs and outputs from the specifications.
  2. Derive the truth table for each of the outputs based on their relationships to the input.
  3. Simplify the boolean expression for each output. Use Karnaugh Maps or Boolean algebra.
  4. Draw a logic diagram that represents the simplified Boolean expression. Verify the design by analysing or simulating the circuit.

Examples

Specification

Design a circuit that has a 3-bit binary input and a single output (Z) specified as follows:

  • Z = 0, when the input is less than 510
  • Z = 1, otherwise

  1. Determine the inputs and Outputs

    1. Label the inputs (3 bits) as A, B, C
      • A is the most significant bit
      • C is the least significant bit
    2. The output (1 bit) is Z
      • Z = 1 -> 1012, 1102, 1112
      • Z = 0 -> other inputs
  2. Derive the Truth Table

  3. Simplify the Boolean Expression

    From the truth table, we use one of the following 2 methods to obtain the simplified boolean expression

  4. Draw the logic diagram

    Draw a logic diagram that represents the simplified Boolean expression. Verify the design by analysing or simulating the circuit.

Specification

Design a BCD to 7 segment decoder circuit for segment e that has a 4-bit binary input and a single output (7e) specified by the truth table

  1. Determine the inputs and Outputs

    1. Label the inputs (4 bits) as A, B, C, D
      • D is the most significant bit
      • A is the least significant bit
    2. The output (1 bit) is 7e - segment e of 7 segment display
  2. Derive the Truth Table

    Obtained from the BCD to 7 segment decoder truth table. Note that 7e is obtained from column e.

  3. Simplify the Boolean Expression

    From the truth table, we use one of the following 2 methods to obtain the simplified boolean expression

  4. Draw the logic diagram

    Draw a logic diagram that represents the simplified Boolean expression. Verify the design by analysing or simulating the circuit.

More Examples

Bank Alarm

A bank wants to install an alarm system with 3 movement sensors.

To prevent false alarms produced by a single sensor activation, the alarm will be triggered only when at least two sensors activate simultaneously.

Prime Number Detector

Design a circuit that has a 3-bit binary input and a single output that

  • output 1 if it is a prime number. eg 210, 310, 510, 710
  • otherwise output 0.

Compare two 1-bit numbers

Given two input bits A and B, produce three outputs X, Y, and Z so that

  • X is 1 only when only when A > B,
  • Y is 1 only when A < B, and
  • Z is 1 only when A = B