# Math Help - basic boolean logic

1. ## basic boolean logic

Hello, I just want to confirm a few boolean logic questions.

1. Both the inputs to a NOR gate are A the output will be :
A / NOT A / unknown.
I think the answer should be "NOT A".

2. If a three input NAND gate has two inputs connected to a +5V and the third input to A, the output will be:
A / NOT / unknown
I think the answer should be "NOT".

3. If one input to a NOR gate is HIGH and the other inputs are unknown, but could be either HIGH or LOW, the output is:
HIGH / LOW / UNKNOWN
I think the answer is "LOW".

Thank you for any confirmation that I am on the right track.

2. ## Re: basic boolean logic

Hey, I worked it myself and I got the same answers.

Number 2 is NOT A, right?

3. ## Re: basic boolean logic

Originally Posted by jll90
Number 2 is NOT A, right?
Does +5V mean True from the standpoint of logic? Then yes, the answer is NOT A. True AND True AND A = A, so NOT (True AND True AND A) = NOT A (assuming I understand correctly what a three-input NAND gate is).

4. ## Re: basic boolean logic

In terms of boolean algebra:
i). The output of a NAND gate with inputs a, b is $\overline{ab}=\overline{a}+\overline{b}$

ii). The output of a NOR gate with inputs a, b is $\overline{a+b}=\overline{a}\overline{b}$

1. A and A into a NOR gate yields $\overline{A}\,\overline{A}=\overline{A}$ = not A

2. Does a+5V mean the output of running a through an inverter? If so, the 3 inputs to the NAND gate are $\overline{a}, \overline{a}\,\, and A$ and then output
$\overline{A}+\overline{\overline{a}}+a=\overline{A }+a$ Is there unstated relationship between a and A, for example $A=\overline{a}$. If so, the answer is a, otherwise unknown.

3. Any relationship between LOW and HIGH, e.g. $HIGH=\overline{LOW}$ ? If so, output is
$\overline{HIGH}+\overline{X}$ with X either HIGH or not HIGH. But even here, you get unknown.

I think the best way to deal with the logical gates is with boolean algebra. I hope your instructor or text book is more explicit on exactly what the situation is.