Question

pretty please: anyone any good at these...?



convert binary to decimal:
1100
1010
11100
10000

Answer 1

\(\large 1100 = 0 \times 2^0 + 0 \times 2^1 + 1 \times 2^2 + 1 \times 2^3\)

Answer 2

each position to the left, increases the position value by a factor of 2

Answer 3

ok... so 1100 is 0048, so 48?

Answer 4

\(\large 1010 = 0 \times 2^0 + 1 \times 2^1 + 0 \times 2^2 + 1 \times 2^3\)

Answer 5

or 4+8 = 12?

Answer 6

Let's think backwards of what we're trying to do first since we're all more comfortable with base 10.

What are all the places called? ones, tens, hundreds, thousands, etc... do you notice a pattern here? Every digit is really just 10 raised to a power.

So, \[ones \ place=10^0\]\[tens \ place = 10^1\]\[hundreds \ place = 10^2\]\[thousands \ place = 10^3\] etc...

So if you have the number 324 that's really just \[(3*10^2)+(2*10^1)+(4*10^0)\]

It's the same thing with binary, except that you are using 2's instead of 10's!

Answer 7

1100 is 2^3 + 2^2 + 0 + 0 = 12

Answer 8

^^above Kainui's explanation...

Answer 9

gotcha, so following yours and kanui's explanation:
1010 = 0 + 2 + 0 + 8 = 10
is this right?

Answer 10

yup

Answer 11

sweet, cheers man, final confirm:
11100 = 0+ 0+ 4 + 8 + 16 = 28??

Answer 12

right :)

Answer 13

sweeeeeet!
cheers @ganeshie8
cheers @kainui
u guys rock!