Full Adder Test Circuit PDF

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Fundamental building block of an ALU (Algebraic Logic Unit....

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ELEN 305 Digital Logic Design Lab 3: A Simple Minterm/Maxterm Example and a Full Adder Test Circuit I.

II.

Purpose The purpose of this lab will be to implement a simple two input minterm/maxterm example. Equipment a. b. c. d. e. f. g.

III.

IV.

Logic Gates 7404, 7408, 7432 Logic Switches Wire Breadboard or Power Board Power Supply if using Breadboard LEDs Digital Multimeter

Procedure Wire Figure 1 and test it using inputs from switches and verify that F(A,B) is as shown. [The circuit in Figure 1 implements the minterms F(A,B) = m1 + m2 + m3.] Verify that the truth table is as expected. Wire Figure 2 and test it using inputs from switches and verify that G(A,B) is as shown. [Figure 2 is designed to implement the maxterms G(A,B) = F’ = M 0.] Verify that the truth table is as expected. The results should be the same as in Part A Results Algebra for Figure 1: =A’B+AB’+AB =(A’+AB)(B’+AB) + AB’ =(A+(A’+AB)(B+AB))(B’+A’+AB)(B+AB)) =(A+A’+AB)(A+B+AB)(B’+A’+AB)(B’+B+AB) =(1+AB)(A+B+AB)(B’+A’+AB)(1+AB) =(1)(A+B+AB)(B’+A’+AB)(1) =(A+B+AB)(A’+B’+AB) =(A+A+B)(A+B+B)(A+A’+B’)(A’+B+B’) =(A+B)(A+B)(1+B’)(A’+1) =(A+B)(1)(1) =A+B

Figure 1 Input A 0 0 1 1

Input B 0 1 0 1

A’ 1 1 0 0

B’ 1 0 1 0

A’B 0 1 0 0

AB’ 0 0 1 0

AB 0 0 0 1

A’B+AB’ 0 1 1 0

A’B+AB’+AB 0 1 1 1

Minterm m0 m1 m2 m3

Algebra for Figure 2 (A’+B’)’ A’’+B’’ A+B

Figure 2 Input A 0 0 1 1

Input B 0 1 0 1

A’ 1 1 0 0

B’ 1 0 1 0

(A’B’) 1 0 0 0

(A’B’)’ 0 1 1 1

Maxterm M0 M1 M2 M3

Minterms and Maxterms are a compact way of expressing Boolean function values. “In general, a minterm of n variables is a product of n literals in which each variable appears exactly once in either true or complemented form.” For example, a minterm of variables A, B, and C, is a product (A*B*C), where each literal will be represented as a 1 or 0 by writing [X] or [X’]. When a function is written in Sum of Products form it is also written as a sum of it’s minterms. Minterms are represented by a lowercase m and a subscripted decimal number. Minterms not only provide a compact way of expressing a formula but also make possible simplification methods such as using a K-Map.

Maxterms are similar to minterms as far as their uses however a maxterm is a product of n literals. And when a formula is expressed using maxterms it is said to be written in Product of Sums notation.

Simplification of logic circuits is fundamental to the improvement of digital designs. As a result of simplifying a logic circuit the complexity, number of components, cost, size, and energy requirements of the circuit are reduced. Furthermore the speed and reliability of the circuit increase....