"ELECTRICAL AND ELECTRONICS ENGINEERING" LAB INVESTIGATION II "COMBINATIONAL LOGIC GATES CIRCUITS"
Student Name: MAHROO URIS Student ID: SCM030782 Lecturer Name: Mr Chris
Introduction:
In digital circuit theory, combinational logic is a type of digital logic which is implemented by Boolean circuits, where the output is the pure function of the present input only. A lengthy expression of a combinational logic gates can be simplified to produce a much simple circuit that produces the same output Simplification is about reducing the number of logic gates for the same function but will still yields the same output. Simplification is necessary to ease the construction of the logic circuits and avoid complicated and confusing circuit. Since the number of gates is reduced in the simplification, the speed increases and the power consumption and dissipation reduce significantly. Simplification can be performed using Boolean algebra or Karnaugh Map.
Objective:
To simplify the given set of Boolean equation
To construct the combinational logic gates circuit based on the equation.
To observe the output similarity og the logic equation before and after the simplification and the advantages of the simplification.
Apparatus:
Digital Logic Lab KL-31001 (c/w CLK generator, LED indicator for LOGIC output, INPUT toggle switches, 5V DC power supply)
Digital IC 7400 (NAND gates), 7408 (AND gates), and 7432 (OR gates).
Connecting wires.
Logic Circuit Diagram:
Figure (a) shows combinational logic diagram.
Figure (a)
Figure (b) shows simplified logic diagram.
Figure (b)
Procedure:
We were required to implement the combinational logic gates circuit diagram as shown in Figure (a) using the apparatus provided to us in the lab.
The four digital inputs (A,B,C and D) were then applied and the output of the circuit is to be taken according to the order of the inputs.
The simplified combinational logic gates circuits was then constructed as shown in Figure (b)
Once again, the output of the circuit was taken when the three digital inputs (B,C and D) were applied.
Results: Inputs and outputs:
A 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1
B 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1
C 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1
D 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1
X 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0
Table © shows the truth table for the logic diagram as in Figure (a)
B 0 0 0 0 1 1 1 1
C 0 0 1 1 0 0 1 1
D 0 1 0 1 0 1 0 1
X 0 0 0 1 0 0 0 0
Table (d) shows the truth table for the simplified logic circuit diagram as in Figure (b).
Discussion: For both the parts of experiments, before and after simplification of combinational logic gates, the output value is always in two binary numbers 0 and 1. For this particular experiment, we took 0 as the result when the LED light remained off and 1 as a result whenever the LED lights up. For figure in (a) we found out that there are two cases where LED light lights up. Indicating 1 as a result. For figure (b) there was only one case where LED lighted up, for others it remained off. The output X equals to 1 was at the same digital input for before and after simplification and this was clearly the case where both circuit showed output of 1.
Conclusion: In this experiment we conducted. We achieved all the objectives and all the output results we got were accurate to initial calculated values as well as theory of Boolean equation. Less connecting wires can reduce any time delay etc. The aim of this experiment was achieved.
References:
Thomas L. Floyd, 2006, Digital Fundamentals, 9th Edition, Pearson Prentice Hall, Chapter 3 and Chapter 4 on Logic Gates, Boolean Algebra and Logic Simplifications,pp. 112-225
Tocci, R, J, Widmer, N, S and Moss, G,L, 2007, digital Systems and Principles and Application, 10th Edition, Pearson Prentice Hall, - Chapter 3 and 4 on describing Logic Circuits and Combinational Logic Circuits, pp, 54-193.
