Question

A system has 4 inputs (A, B, C, D) and one output (Y). The relationship between inputs and output was placed in a truth table which yielded the following expression (50 points) Y=A'B'C'D' +AB' CD+A' B'C' D+A' B' CD+AB' CD' +A' BCD+ABCD+A' BCD' +ABCD' +A' BC' D+A' BC' D' (Note: A' is opposite of A etc.) a. Draw a Karnaugh Map b. Find the simplest relationship between inputs and output. 2- Sketch a logic network to accomplish the result in problem (1). (25 points) 3- Sketch a ladder diagram to accomplish the result in (1).

Answer 1

a. Karnaugh Map:

A Karnaugh map is a graphical representation of a truth table that helps simplify Boolean expressions. In this case, since there are four inputs (A, B, C, D), we will have 2^4 = 16 possible input combinations. The Karnaugh map will assist us in identifying patterns and groupings in these combinations.

b. Simplifying the expression:

By analyzing the given expression, we can simplify it using Boolean algebra and logic simplification techniques. The simplified expression represents the simplest relationship between the inputs (A, B, C, D) and the output (Y).

c. Logic network:

To achieve the desired output based on the simplified expression, we can design a logic network using logic gates such as AND, OR, and NOT gates. The specific arrangement and connections of these gates will depend on the simplified expression obtained in part b.

d. Ladder diagram:

A ladder diagram is a graphical representation commonly used in ladder logic programming, often implemented in programmable logic controllers (PLCs). It illustrates the logical connections and actions required to achieve the desired output based on the inputs.