Question

Binary,


I can't understand How I go from the first line to the second? http://screencast.com/t/xtMveJaOmatd

Answer 1

basically its a technique to convert a binary number to decimal

Answer 2

if you are given a binary number like 1 0 1 1 0 1
and you want you to find its decimal equavilant quickly then put the weight of each binary digit on its top like...

Answer 3

But why I cant apply this to it in order to convert it? http://screencast.com/t/HYKkQz9vXVF1

Answer 4

Add the numbers that have a 1 below them: -128+64+4+2=-58.

Answer 5

The think is why I can't use the method we were discussing before to solve this

Answer 6

Use whatever method which suits you ..some choose the shortcut way of not explicitly writing down each step rather they just add the weights on top of each number .

Answer 7

I try to apply this method http://screencast.com/t/HYKkQz9vXVF1 but it can't work. The thing is that I can't understand why

Answer 8

It has to do with the -128 weight in your example.
Normally, 8 bits can cover the binary representation of the numbers 0..255, so 256 numbers. The number 198 then has a binary reperesentation of 11000110:

It is:
\(128+64+4+2=1 \cdot 2^7+1 \cdot2^6+0 \cdot2^5+0\cdot 2^4+0\cdot2^3+1\cdot2^2+1\cdot2^1+0\cdot2^0\).

In this case, however, the weight of the first binary digit is set to be -128.
Therefore the number that is described by "11000110" is 198-256=-58.

This way of coding the numbers makes it possible to cover the range of -128..127 in binary.

Answer 9

How do you know that its 8 bits and not 16 for example ??

Answer 10

Silly me.... I got it.

Answer 11

YW!