You have a list of binary numbers, as a character array. So zeros, ones, and a decimal point. (Personally, I think that should be called a bicimal point.) For example:
BiNum = ['0001.1101';'0101.0111';'1000.0001';'0000.1000']
BiNum =
'0001.1101'
'0101.0111'
'1000.0001'
'0000.1000'
If we can assume all of the bicimal points lie at the same location, then it is truly trivial. First, locate the bicimal point.
bicimalind = strfind(BiNum(1,:),'.')
Once we know the location, we can remove them.
BiNum(:,bicimalind) = ''
BiNum =
'00011101'
'01010111'
'10000001'
'00001000'
Finally, reconstitute the numbers in true decimal form, first as integers.
BiNumBits = size(BiNum,2);
DecNum = (BiNum - '0')*2.^(BiNumBits-1:-1:0)'
All that remains now is to put the bicimal point back in, as an effective bit shift.
DecNum = DecNum*2^(bicimalind - BiNumBits - 1)
DecNum =
1.8125
5.4375
8.0625
0.5000
As you can see, fully vectorized. It only required that the bicimal points were in the same position for all numbers. If that was not true, then you would need to work slightly harder, but not a lot. You might do the above proces for every row, separately, in a loop. God forbid, a loop. In fact though, it would not take a lot of effort to do that in a vectorized form either.
A nice thing is, as long as your numbers are limited to no more than 52 bits, then these computations will result in EXACT values for those decimal numbers in double precision. That is because doubles are themselves stored in a binary form internally. In fact, this points out you could have done the above computations by converting the numbers into a proper hexadecimal form, then casting that result into a double. IMHO, probably more mental effort than it is worth, since the above computation was so easy.)
Finally, I would point out that IF your numbers have more than 52 bits, you will not be able to convert them in this way, since a double precision number is limited to 52 bits. Could it still be done, using carefully written code? Of course. I know that to be true, as the guy who has written several high precision arithmetic codes in MATLAB, so I know of what I speak. :)
