Question

Create a truth table and then use Karnaugh map(s) to produce the MPOS equation(s) for a circuit which takes two, two-bit binary numbers, AB, and CD, and outputs their three-bit sum WXY. For this question, only provide the function for the output W. (Use "don't cares" wherever possible.)

Answer 1

The student is working on a logic function simplification using a truth table and Karnaugh map for the most significant output bit of a full adder adding two 2-bit numbers. 'Don't cares' are used in the K-map to simplify the MPOS equation for the output W.

Step-by-step explanation:

The student's question involves the creation of a truth table and using Karnaugh maps to simplify a logic function for a binary addition. The specific request is to determine the function for the most significant output bit (W) of a full adder circuit adding two 2-bit binary numbers (AB and CD). A truth table must be constructed for the possible sums of AB and CD, which will have inputs (00, 01, 10, 11 for both AB and CD) and a corresponding binary output for W (the most significant bit of the sum which would be 0 or 1). After determining the truth table, a Karnaugh map can be used to minimize the logic function to obtain the most simplified MPOS (Maxterm Product Of Sums) equation for W.

When constructing Karnaugh maps (K-maps), "don't cares" are used to further reduce the complexity of the logic equation by filling in positions in the K-map that are not used by the actual function, but can help in grouping the terms more efficiently. This is particularly helpful for digital circuit design, as it reduces the number of gates and complexity of circuits necessary to implement a given logic function.