# Base 2 trouble

by MartinJH
Tags: base, trouble
 P: 64 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
Mentor
P: 37,560
 Quote by 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
Why do you have ones in these terms? "(1 * 2^1) + (1 * 2^0)"
P: 64
 Quote by berkeman 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.

P: 15,294

## Base 2 trouble

 Quote by MartinJH 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 8

Hey lookit that. I can look down and see Berkeman slooooooowly tyyyyping away.....
Mentor
P: 37,560
 Quote by MartinJH 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?
 Mentor P: 37,560 Dagnabit! Beaten by Dave again
 P: 64 OK, thank you guys I understood :).
PF Patron
Thanks
Emeritus
P: 38,387
 Quote by 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.
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.
P: 64
 Quote by HallsofIvy 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 ignoring the 1 in 1 * 2^3 as it was simply telling what binary digit 2^3 was representing.
 P: 1,781 There are 10 kinds of people in the world. Those who read binary and those who don't.
Mentor
P: 19,675
 Quote by Antiphon 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.
P: 64
 Quote by Mark44 Or, there are 3 kinds of people in the world: those who understand mathematics, and those who don't.
I don't

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