00:02
We are going to use exodecimal notation to represent the following bit patterns.
00:08
Part a, 011 -0101011 -1 -1 -0 -1 -0 -0 -1 -0.
00:16
In part b, 11110101, 4 times 0 -1 -1 -1 -1 -1 -1, and in part c -1 -0 -0 -0 -0 -0.
00:28
That is we have numbers the bit patterns are numbers in binary base in base 2 and we're going to pass those numbers to base 16 that is exodecimal for that we use the following fact we use the fact that four bits or four binary digit is equivalent to one x decimal digit.
01:08
In fact, using these four binary digits, we can reproduce all 15 xadecimal digits.
01:18
Remember that base 16, which is what we call exadecimal base, have 16 digits.
01:32
We have 0 up to 9 as in base 10 digits.
01:40
And then, because 16 needs 16 digits we got to use letters to represent those digits equivalent to 10 11 12 13 14 and 15 so we get a b c d c d e and f so these are the x decimal digits a representing 10 be representing 11 c 12 d 13 e 14 and 15 and so we can write a table of four binary digits represented each exodecimal digits so number one will be 0001 number two will be 0 010 number 3 will be 0 011 that is because if we transform this binary patterns into decimal we get these numbers here and we can going on this way to obtain the following table here it is we have then this table of exodecimal numbers that's our digits in terms of patterns of four binary digits as we can see here we can represent all 15 or all 16 digits zero i didn't put but of course number zero is all patterns equal zero so we can represent all digits in base and 16 asset pattern of four binary digits.
03:30
And with that table, then we can transform these patterns, these speed patterns into x -decimal notation.
03:38
For that, we separate in groups of four digits from right to left, each of these patterns.
03:51
So let's start in bar with 011, 0101, 0, 4 times 1, 0, 0, 10.
04:25
So we are going to separate from right to left.
04:27
It's very important that we start from the right of the number in groups of four digits.
04:33
So we get this four and this four, this four, this four, and this four.
04:39
In this case, we complete the group of four digits and there is no group of less than four digits.
04:47
If that happens to the left, we complete with zeros to have the last group of four digits.
04:53
Digits.
04:55
Okay, so now we look at the table and we have this digit 0101, sorry, this on the left, 0110, and we look at the table that number.
05:10
We have it here, it's six, and we have 1 .1010, this one here, that's a, then all ones is f, as we see here, and 010, 010, is 2 so we can say that the pattern 0111011110 1111 1 0 0 base 2 is the same as 6a f2 base 16 as we can see we need of course less tigit base 16 to represent same number that that as the reason why in computers it is often used the xisml notation.
06:16
So in part b, sorry, we are a haptive pattern.
06:20
I'm going to write it completely at this moment.
06:25
So we have this pattern here and we group in packs of three or four digits from right to left...