For this module you will design some simple digital circuits based on Boolean expressions. Draw circuits that implement the following Boolean expressions using some combination of AND, OR, NOT, NAND, and NOR gates. (I recommend you draw your circuits on white paper with black pen, scan the images, and paste them into your Word document.)
- NOT X OR NOT Y OR Z
- X OR Y OR NOT Z
- NOT X AND Y OR NOT Y AND Z
Write a paper discussing your design. Please include the following:
1. Diagrams of your logic circuits.
2. Truth tables that indicate the output (a 0 or a 1) for each possible combination of values of X, Y, and Z.
3. A clear explanation of the relationship between Boolean Algebra and the circuits that you designed.
I have worked out the given job in a separate word file as you requested to do and I also have generated one pdf file for the same. ( I Recommend you to download the attached files to see the Final solution.)
The OR gate is shown ...
The OR gate can be represented by addition in the Boolean Algebra. For example if two inputs x, y are used with OR such that, X OR Y then logically, it can be shown as X + Y.
The AND gate can be represented by multiplication in the Boolean Algebra. For example if two inputs x, y are used with AND such that, X AND Y then logically, it can be shown as X.Y.