Blog posts of '2014' 'November'

Boolean equation truth table

Q. I am studying Lesson 5516. In Appendix A-5 in the back of the lesson there is a sample problem. It starts with a Boolean equation you are supposed to use to fill out a truth table. I don’t know how to do this.

A. Each term in the Boolean equation describes where ones are to be put in the output column of the truth table. For example, the first term in the equation is AB. This means that Whenever A is zero and B is one, there is a 1 in the output column, regardless of the states of C and D. So you put a 1 in the output columns where A, B, C, and D are 0100, 0101, 0110, and 0111. The next term is ABCD, with all the terms NOT-ed. This means that where A, B, C, and D are all zeros, we have a 1 in the output column. Only one line of the truth table meets this condition: the first one, where ABCD are 0000.

The next term is ABCD. So We put a 1 in the output column for 1111. In the last term we have A,B, C, D. This means that we put a 1 in the output column for 1011. Note that where there are four letters in a term, it refers to only one line in the truth table. Where there are three letters, two lines of the table will be involved. Where there are two letter, it refers to four lines of the truth table. If there is a one-letter term, eight lines will have a l in their output column.