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Old 02-01-2011, 05:01 PM   #1
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Default Looking for an online tutor (Logic Design)

I'm currently in a logic design class at my University. In my opinion, the teacher sucks at teaching, and it's unfortunate that he is the only one teaching the class. He doesn't teach the class that quite well. I can figure out some by myself after reading the book, but there will be times that I will not understand.

This is what the class covers
Quote:
1. Number systems, conversions, and binary arithmetic
2. Boolean algebra and gates
3. Algebraic Simplification
4. Karnaugh map minimization of boolean functions
5. Quine-McCluskey minimization of boolean functions
6. Combinational network design
7. MSI components
8. Introduction to hardware description language
9. Latches, flip-flops
10. Synchronous sequential circuit analysis
11. Synchronous sequential circuit design (synthesis)
12. Algorithmic state machine (ASM) design techniques
13. Analysis and synthesis of asynchronous sequential circuits
So if anybody know how to do any of these topics, and want to help me, please say so. I am willing to pay hourly through paypal.

I think we are currently in "Algebraic Simplification". Here is a question from my book.
Quote:
Use algebraic manipulation to prove that xy+yz+x'z = xy+x'z.
I'm not asking for you guys to give me the answer to the problem. If you know how to solve this, please help me.
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Old 02-02-2011, 08:41 AM   #2
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Default Re: Looking for an online tutor (Logic Design)

I'll dig out my notes from uni.
(i've been meaning to go through these and re-learn lots that I've forgotten anyway).

I can't really devote endless amounts of time to this though.
and I wouldn't be too bothered about being paid since this is something that I want to go back over myself!

one little thing though.

the problem that you posted
xy+yz+x'z = xy+x'z.

you've put ' I assume to incidate a not line that would be written over the letter if you were writting it by hand, or using a program like mathtype that can present things like this

e.g on paper not x would look like
_
X

if you say the equation you posted out loud,

is it
x and y OR y and z OR x and NOT z
or is it,
x and y OR y and z or NOT x and z

basically, is your single quote applying to the letter before or after?

It's easier to avoid the confusion and use

+ = or
. = and
/ = not (and is placed preceeding the letter or expression that it applies to.

e.g
x . y = 1
x and y = 1
/x . y = 1
not x and y = 1
/(x . y) = 1
not x and not y = 1
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Old 02-02-2011, 10:54 AM   #3
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Default Re: Looking for an online tutor (Logic Design)

Cool, thanks.

My teacher told me...
_
x and x' are prime numbers, never saying anything about "not". So if I used "/" for prime numbers, then the equation would be xy+yz+/xz = xy+/xz.

I figured out I had to use the consensus theorem for this problem. I apparently found the answer on Wiki. However, I can't quite understand how to do it.

The first line to solving this was
LHS = xy + /xz + (x + /x)yz
Did the x and /x get put into parenthesis because they are one of a kind?
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Old 02-02-2011, 11:27 AM   #4
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Default Re: Looking for an online tutor (Logic Design)

you're learning boolean algebra right? for the purpose of logic (learning about circuits and logic gates etc)
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Old 02-02-2011, 12:06 PM   #5
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Default Re: Looking for an online tutor (Logic Design)

Yes, I am currently learning boolean algebra.
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Old 02-03-2011, 04:33 AM   #6
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Default Re: Looking for an online tutor (Logic Design)

ok...

I'll try to start with the basics. (which is probably stuff you already understand).


in regular algebra a letter is a symbol for an unknow number

eg, 1 + x = 2 and you know that x is one.


in boolean algebra, the letters stand for states, that will give a particular logic output. (1 or 0)

there are four symbols

a dot (.) is AND (both)
a plus (+) is OR (either)
a slash (/) is NOT (and in that one, but not that one) (if you were writting it on paper a line over the top is recognised as not). (as a not this is also called a prime)


other than that it works almost exactly the same as normal maths.

for example 2 * 3 = 6 and 3 * 2 = 6 also 6 = 3 * 2

2 + 3 = 5 and 3+2 = 5


in boolean algebra this still works exactly the same


x . y = y . x
x + y = y + x

that's the commutive law.



you use parenthesis to denote the grouping of expression

for example in regular maths
2(3+5) = 16
you're basically grouping the 3+5 and then applying the part that comes outside the brackets.

it works the same way in boolean algebra

a . (b+c)

= a . b + a . c

"A and B or C" is the same as "A and B, or A and C"

you can also use brackets to apply a logic function to what's in the brackets.

A . /(B+C)

A and not B or A and not C

and just like regular algebra
(1 + 2)(3 + 4) = 1 * 3 + 1 * 4 + 2 * 3 + 2 * 4

the same is also true of boolean algebra

(a+b).(c+d) = a.c + a.d + b.c + b.d
that associative law


then there is identity laws, which again work just like normal maths.
a + 0 = a
a . 1 = a

To be honest, I really feel that that is actually all you need to know about boolean algebra in relation to logic states. that enables you to identify black box logic circuits.


there is the complimentaty laws,
A + /A= 1
and A./A = 0

the prime of a prime is zero
/a . /a = 0

and primes cancel each other out
//a = a
(not not A), doub le negative there


then there is demorgans law

if you have the prime of two states /(ab) this is the same as writting /a+/b




Next....
in it's simplest it's easiest to think of this in terms of a light bulb and a set of switches.

lets say I have two switches,
switch a, and switch b

if I turn switch a off the light goes off
if I turn switch a on the light comes on, it doesn't matter what position switch b is in.

to express this in boolean algebra I can

if switch A is on, and switch B is on, the light is on

A.B= 1

or, another set of switch positions that will turn the light on
a = on, b = off

A./B =1

so there are two states that the switches can be in to turn the light on
a and b both on, or a on and b off

A.B + A./B = 1

if you look at this equation it's quite easy to see that a.b or a./b can be reduced just to A=1.

then you see that it's only switch A that does anything.

here's a slightly different explanation of the gates and how to form equations
Boolean arithmetic : BOOLEAN ALGEBRA
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Old 02-06-2011, 08:45 PM   #7
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Default Re: Looking for an online tutor (Logic Design)

I see. It's starting to make sense. You left out "the one with no name" and the "consensus" theorem though.

I'll try to solve some problems from the book again to see if I can do it. I will either post here or PM you when I need some help.

Thanks again.
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Old 02-07-2011, 06:13 AM   #8
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Default Re: Looking for an online tutor (Logic Design)

I just thought of a better way to put that reduction than you can just see that it happens like that.

A.B + A./B = 1

is re-arranged (factored) to A . (B + /B)

Complimentary law says
B + /B= 1

so we have A . (1) = 1

identity law says
A . 1 = A

so just A = 1

which is the mathematical way of explaining it, not saying it's just obvious! (which is was)
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