Experiment - analysis of digital circuits objective - to

Question

Experiment - Analysis of Digital Circuits

1. Objective - To practice the analysis of digital circuits using Boolean algebra and other methods.

2. Analysis - Perform the following analyses for one of the ten given circuits.

1. (a) Remove all the internal bubbles and bubbles at the outputs in the circuit by applying DeMorgan's theorem so that the circuit consists of only AND gates and OR gates, and INVERTERS. INVERTERS can only be used for the inversion of inputs.

(b) Redraw your circuit using the given gates. They consist of four INVERTERS which are used for A', B', C', and D', four 3-input AND MN gates, four 2-input AND gates, four 3-input OR gates, and four 2-input OR gates. Draw your circuit in the bottom half of the schematic template.

Minimize the number of gates in your circuit by removing duplicate gates. Use G₁, G₂, G₃, G₄, G₅, and G₆ for the outputs of your circuit. If your circuit is correct, the value of G_i should be the same as that for F_i for i = 1 to 6.

2. (a) Determine the simplest product-of-sums (POS) expressions for G₁ and G₂.

(b) Determine the simplest sum-of-products (SOP) expressions for G₃ and G₄.

3. (a) Find the maxterm list forms of G₁ and G₂ using the product-of-sums expressions in step 2(a).

(b) Find the minterm list forms of G₃ and G₄ using the sum-of-products expression in step 2(b).

4. (a) Find the minterm list forms of G₁ and G₂ using the maxterm list forms of G₁ and G₂ obtained in step 3(a).

(b) Find the minterm list forms of G₅ and G₆ using the minterm list forms of G₁ and G₂ obtained in step 4(a).

5. Assume that AB = 01 (A = 0 AND B = 1) never occurs as inputs, find the minterm and maxterm lists for G₁, G₂, G₃, G₄, G₅, and G₆.

Verify your answers in steps 3 - 5 by comparing the values of G₁, G₂, G₃, G₄, G₅, and G₆ with the values for F₁, F₂, F₃, F₄, F₅, and F₆ in the schematic template.