Understanding Electronics Basics #2

[Muttley600]

Finally, I have two days off
I've read two links on logs, on last link now but read that as first link, I keep getting distracted
Do you know, I didn't have a clue what magnitude meant, it's just the power of/exponent, I did say I was getting tripped up by not relating words to meanings, I have also just read up on base numbers

Now here's where I look like a complete dummy again.lol
Are they saying a base number keeps climbing at that specified rate
0,1,2,10,11,12,20,21,22 etc for base2 & is that why we get a plot on graph with base number of 2n

I think I have that right, again never seen anything described like that before

Hope your both well & have recovered from all my questions so far so I can ask more.lol

So a base number is also called a indice or index number.....how many names can they give the same thing?

So Im getting mixed up already, indice is exponent not base num......hold on, I'm confusing myself, they wouldn't call the exponent the base number would they, wouldn't that be backwards or am I being too logical?

They blinking well are aren't they, no wonder I'm taking ages to understand it all

I'm nearly there, all week Inbetween work for about 4hrs reading, by tomorrow, I will understand logs & how they work
But for tonight, I'm shattered

 

[cowboybob]

We'll be here when you need us.

 

[KeepItSimpleStupid]

Magnitude: is "how big". An order of magnitude is a 1 power of 10 or 10. 3 orders of magnitude is 10 * 10 * 10 or 1000.

Base 2: I don;t know what your trying to say.
Let's try counting in base 2.

000 001 010 011 100 101 110 111; that's counting from 0 to 7 decimal. Note that numbers "carry" just like they do in base 10 except with the following rules: 0+0 = 0; 0+1 = 1; 1+1 = 0 carry 1 or 10
so
101+
001=
110; the last digits or lsd is 1+1 which gives a 0 + 1 to carry
LSD is Least Significant Digit

Powers of 2 are:
1 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768 65536
That's all I know by memorizing. That's 2^0 to 2^16
In the true sense of the word, a power of 2 should be in base 2, thus

0001 0010 0100 1000 etc, just like the power of 10 in base 10 is 1 10 100 1000 etc. These numeric characters represent the quantity when you consider the base of 10 and 2. Your not allowed to call the base 2 "0010" Ten though.

---

Base is at the bottom; so for a number B^n; B is the base and n is the exponent.
BEWARE: The base does not have to be an integer like 2 or 10. In fact, Base e is common. That number is 2.(something that never ends).
BUT the E in 1E10 has no relation to little e.

 

[cowboybob]

Flashback...!

I still have two of my old slide rules (both Picketts, one white and one yellow). And I can remember that I frequently had to find a Log[SUP]e[/SUP] on them.

But durned if I can remember how...

Or for that matter, why

Can't find, however, my HP Programmable Scientific. And long since used the programming strips for floss.

 

[Muttley600]

Morning CBB, need to be on computer to reply to KISS
Going for a walk then shall have another go but this is like learning a new language, interesting to see how it works
Need to sit down with calculator as all these different meanings are all making one complete story aren't they
I even get the binary thing now
I just need to finish reading about logs & update my folder while it's all fresh in my mind
Don't know how but binary seems to relate to my picture brain.lol scary when I find numbers & words hard to see in their proper format, but they seem totally logical

 

[Muttley600]

Flashback...!

I still have two of my old slide rules (both Picketts, one white and one yellow). And I can remember that I frequently had to find a Log[SUP]e[/SUP] on them.

But durned if I can remember how...

Or for that matter, why

Can't find, however, my HP Programmable Scientific. And long since used the programming strips for floss.

lol, I quite fancy getting a better calculator, but how often do you use stuff like this?
I suppose it depends in what you are doing or calculating

 

[KeepItSimpleStupid]

Do you want to try to understand negative numbers in base 2? Subtraction?

 

[Muttley600]

Do you want to try to understand negative numbers in base 2? Subtraction?

Hiya KISS
yes, but let me catch up first **broken link removed**

I finally get a day off, do a 7 mile walk in the countryside with Lou & Bobby & promtly fall asleep, family happy again
catching up slowly, it's more a time issue than anything else, now you see why I was so eager when I had my weeks off

Tell you what thou, this is soooooo much easier on computer than fumbling around on phone screen, but hey, guess I wouldn't even get on hardly at all without phone so who am I to grumble

 

[Muttley600]

ok, lets go through this before I go back to finishing reading about logs

Magnitude: is "how big". An order of magnitude is a 1 power of 10 or 10. 3 orders of magnitude is 10 * 10 * 10 or 1000.

Got that

Base 2: I don;t know what your trying to say.
Let's try counting in base 2.

000 001 010 011 100 101 110 111; that's counting from 0 to 7 decimal.
Note that numbers "carry" just like they do in base 10 except with the following rules: 0+0 = 0; 0+1 = 1; 1+1 = 0 carry 1 or 10
so
101+
001=
110; the last digits or lsd is 1+1 which gives a 0 + 1 to carry
LSD is Least Significant Digit

Sorry, I gave a half understood example, what your saying after reading makes perfect sense

Powers of 2 are:
1 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768 65536
That's all I know by memorizing. That's 2^0 to 2^16
In the true sense of the word, a power of 2 should be in base 2, thus

This is what tripped me up, I understand power of/exponents completely, but this base number counting is still up in the air simply because its new, I need time to nail down which numbers are moving now, I understand the counting up, just not what is counting up because I havent read all of the info yet

0001 0010 0100 1000 etc, just like the power of 10 in base 10 is 1 10 100 1000 etc. These numeric characters represent the quantity when you consider the base of 10 and 2. Your not allowed to call the base 2 "0010" Ten though.

I'm seeing base 10 & 2 are the only ones that have 0 & 1 in, all other bases have different numbers in

In fact, Base e is common. That number is 2.(something that never ends).
BUT the E in 1E10 has no relation to little e.

This must be where I haven't caught up yet, my calc has log & log2
Which is which, I'm thinking log is for base ten


let me finish reading then ask Q's **broken link removed**

Lost computer to the love of my life for tonight, that'll teach me to smoke.lol
Ok, base & exponent = numbers counting up
What do you mean when you say 2 never stops? Why is it different to any other number?

 

[Muttley600]

So if I'm reading this right, a log is simply the base number (*by exponent)
So to work out cube of 55, I would have to see what base number makes 55 then divide by 3 to give you your answer, don't tell me, I've been reading when I can all week to get you your answer, but you can tell me if my understanding is now correct
Just got to walk bobby & wash up, back in a bit

You can prob tell I haven't finished reading yet

Just before I wash up, so a log is simply counting up in that base number (by that amount, as per your 2example) by however many times the exponent is

 

[KeepItSimpleStupid]

e: https://www.wolframalpha.com/input/?i=base+e

Approximately 2.71828... Just like ∏ ~= 3.1415926..., but unlike 1/3 = 0.3333333.... The last is a repeating decimal. e and ∏ never repeat.

Power of two is nothing but [latex]2{}^{n}[/latex]

 

[Muttley600]

I've finished reading but am still not seeing what I'm looking for, will carry on tomorrow
I'm missing something important in my understanding here

My calcs so far as follows:
1T= understanding
0.1T=little understanding

I put myself at about 0.7T of the way there, I will be at 1.0T tomorrow

 

[KeepItSimpleStupid]

Hint: Concentrate on LOG base 10 first.

 

[KeepItSimpleStupid]

[latex]10{}^{-1}10^{3} = ?[/latex]

[latex]\frac{10{}^{3}}{10^{-2}} = ?[/latex]

[latex]100^{\frac{1}{2}} = ?[/latex]

[latex]100{}^{(1-n)} = 5[/latex]; What is n?


Before you can really understand LOGs, you have to understand the rules of exponents. If you can do the first 3 problems, we are almost there.

The 4th problem can be solved via LOGs. I didn't try to solve it. The first thing you do is to take the LOG of both sides.

LOG base 10 and LOG base e are pretty much the important bases. I did once, but I can't remember how, convert a number base 10 to log base 2. It was useful when I wanted to know what the nearest power of 2 was for a binary search.

So, you might have to forget for the time being that LOG10 exists and look at the "rules for exponents".

For these rules to work, the base has to be the same:

To multiply, you add exponents.

If you can do this problem USING LOGS, we are there:

[latex]1.6^{3}+2.7{}^{3.2}[/latex]

This one is a really tough problem and there are two ways that I know to do it. I'd have to brush up on my skills to do it. I don't expect you to be able to do it.

I have purposely ignored higher powers of x like x^2, X^3, X^4 etc. because except for squaring things, it normally doesn't come up in electronics. I do see now, where some of this provides a foundation even though it's not normally used.

 

[Muttley600]

0.9 there, I have all the pieces & the jigsaw is complete, the strange part is, we have touched on this before butmy lack of maths stopped me seeing the final hurdle (& it is a picture )

It is as simple as 0 = 1
Why E = mc^2
Why everything & anything can be measured

You will see I couldn't sleep last night when after lying in bed for 2 (how ironical.lol) I suddenly saw the whole thing, the complete picture........you have showed me more than logs, I have finally reached the top of the mountain I have been climbing these last few months, the view isn't anything like what I expected. I feel very small & humble now, just a tiny part of this universe

I see there is still a journey ahead, but it all downhill from here, it is now simply a case of exploring the different paths on the way down instead of racing past them to get to the top, to really understand the smaller detail & indulge in the joy of seeing them for what they are

 

[Muttley600]

the last 0.1 is eluding me, I can see what I'm after but i cannot make it make sense, I have been working on this all day
How can e = 7.389
yes, I can see if we use 2.718^2 we get above answer, but it does not relate to the

I know it stands for the base number squared = 1 or 0 if we are calling it base

What am I missing, once I get this, I'll understand, & after working this hard, I cannot settle for 'thats a given'

I know i'm getting distracted from looking at logs but this is important

 

[KeepItSimpleStupid]

I hope your not confusing E=mc^2, e=2171828... and e as in 1E3?

 

[Muttley600]

Don't know??????
I was trying to understand the base & hoping everything else would fall into place, it looked liked the hardest bit to understand, but the numbers aren't adding up?

 

[KeepItSimpleStupid]

You need some sleep and then try to ask your questions again because they didn't make any sense.

 

[Muttley600]

That means I'm on the wrong track.......oh well, back to the drawing board
Ignoring logs for a moment, I know you put a link to base e but how is that working?