Why Is Binary Math Different from Decimal Math?

[MartinJH]

I'm a little embarrassed by this and having a total brain fart.
I understand:
(6 * 10^3) + (3 * 10^2) + (5 * 10^1) + (7 * 10^0) = 6000 + 300 + 50 + 7 = 6357

But for some reason I can't get this:
(1 * 2^3) is equal to 8.

(1 * 2^3) + (0 * 2^2) + (1 * 2^1) + (1 * 2^0) = 8 + 0 + 2 + 1 = 11

 

[berkeman]

I'm a little embarrassed by this and having a total brain fart.
I understand:
(6 * 10^3) + (3 * 10^2) + (5 * 10^1) + (7 * 10^0) = 6000 + 300 + 50 + 7 = 6357

But for some reason I can't get this:
(1 * 2^3) is equal to 8.

(1 * 2^3) + (0 * 2^2) + (1 * 2^1) + (1 * 2^0) = 8 + 0 + 2 + 1 = 11

Why do you have ones in these terms? "(1 * 2^1) + (1 * 2^0)"

 

[MartinJH]

Why do you have ones in these terms? "(1 * 2^1) + (1 * 2^0)"

I copied directly from here;
http://computer.howstuffworks.com/bytes1.htm

Its a page I came across while searching for more information. I did know how to work it out but have forgotten.

 

[DaveC426913]

I copied directly from here;
http://computer.howstuffworks.com/bytes1.htm

Yes, but that adds up to 11, not 8. 1011.

What you started with was 2^3 which is 1000 which is 8Hey lookit that. I can look down and see Berkeman slooooooowly tyyyyping away...

 

[berkeman]

I copied directly from here;
http://computer.howstuffworks.com/bytes1.htm

Its a page I came across while searching for more information. I did know how to work it out but have forgotten.

The thing you copied shows how 0b1011 = 11. (binary 1011 = 11 decimal)

Below that do you see "8 = 1000" listed?

 

[berkeman]

Dagnabit! Beaten by Dave again

 

[MartinJH]

OK, thank you guys I understood :).

 

[HallsofIvy]

I'm a little embarrassed by this and having a total brain fart.
I understand:
(6 * 10^3) + (3 * 10^2) + (5 * 10^1) + (7 * 10^0) = 6000 + 300 + 50 + 7 = 6357

But for some reason I can't get this:
(1 * 2^3) is equal to 8.

So this is what you are reall9y asking about- why 1*2^3= 8?

1*2^3= 1*(2*2*2)= 1*(2*(2*2)). 2*2= 4 so that becomes 1*(2*4). 2*4= 8 so that becomes 1*8= 8.

(1 * 2^3) + (0 * 2^2) + (1 * 2^1) + (1 * 2^0) = 8 + 0 + 2 + 1 = 11

Yes 1011₂ is 1*8+ 0*4+ 1*2+ 1= 11 base 10.

 

[MartinJH]

So this is what you are reall9y asking about- why 1*2^3= 8?

1*2^3= 1*(2*2*2)= 1*(2*(2*2)). 2*2= 4 so that becomes 1*(2*4). 2*4= 8 so that becomes 1*8= 8.Yes 1011₂ is 1*8+ 0*4+ 1*2+ 1= 11 base 10.

I was having trouble working out why 2^3=8. As simple as it seems. I haven't done any sort of to the power maths in years and it skipped my mind.
But yes, you had answered my question, thank you.

But ignoring the 1 in 1 * 2^3 as it was simply telling what binary digit 2^3 was representing.

 

[Antiphon]

There are 10 kinds of people in the world. Those who read binary and those who don't.

 

[Mark44]

There are 10 kinds of people in the world. Those who read binary and those who don't.

Or, there are 3 kinds of people in the world: those who understand mathematics, and those who don't.

 

[MartinJH]

Or, there are 3 kinds of people in the world: those who understand mathematics, and those who don't.

I don't