Need some clarification


#1

Hi guys,

So I am having a hard time getting my head around this chapter. It seems my lack of math skills is haunting me. However, I want to understand this perfectly otherwise I am failing myself. I am generally good with numbers once I understand the basics.

So, let’s start off at the beginning: Base 10 numbers.

I seem to understand this 100% - for example a number like: 123456 can be represented in decimal like so:

1 * 10^5 + 2 * 10^4 + 3 * 10^3 + 4 * 10^2 + 5 * 10^1 + 6 * 10^0

I think this gets me my 123456 number?

Now we go down to base 2 numbers:

What I am trying to figure out is this:

in binary I can work out these two numbers:

A. 10100010 = 162
B. 11001110 = 206

Now how I got this was using the diagram presented to us in this chapter - which looked something like this:

|128 |64 |32 |16| 8 |4 | 2 | 1
| 0 | 0 | 1| |1 |1 |1 | 0 | 0

What I am trying to understand is why is there (from right to left) 1 to 128 in the top?
The pattern shows that we multiply the number to the right by the power of 2 (base 2 numbers) - but if I try follow that rule it goes wrong quickly…

Eg:

1^ 2 = 1
2 ^2 = 4 …so far so good…
4 ^ 2 = 16…

So where does 8 come into it?

If a look at it from right to lift - doubling up each time.

1 x 2 = 2.
2 x 4 = 4;
4 x 4 = 16

Where is 8?

I may have this completely wrong - but I need to understand this…

This is before I get to representing numbers in hex (Base 16) :frowning:

So I need to get the binary part first.

Can anyone shed some light on this more me?

Thanks all


#2

Okay I have figured it out - I was raising the base and not the power…

This would be more correct:

2^0 = 1
2^1 = 2
2^2 = 4
2^3 = 8 (Found you!)
2^4 = 16

Why start with zero though?


#3

[quote=“Tander”]Okay I have figured it out - I was raising the base and not the power…

This would be more correct:

2^0 = 1
2^1 = 2
2^2 = 4
2^3 = 8 (Found you!)
2^4 = 16

Why start with zero though?[/quote]

Never mind - did some reading and it turns out with power when we raise the base to 0 it is always 1. Very odd.