The Language of Bits Part-III

all right so now we have taken a look at boolean algebra which is the manipulation of bits we have taken a look at how positive integers are represented in binary how negative integers are represented in binary so let me maybe just summarize ah at this point so we have for a quick recap boolean algebra had to do with boolean variables so each variable could

take a number between ah sorry not between a number which is either zero or one and we defined basic operations on boolean variables such as the and operation which means that the and function is true only when both the variables or all the variables involved in and operation all of them are one and the or operation is correct only when is true

only when one of the variables is one then we define a not operation that's a compliment and we define an xor operation which is one when one is zero and other is one then we define the binary system to represent positive integers with different basis so the important point to recapitulate you know for ah at this point of the lecture is that

what is the relationship between binary between octal which is base eight and between hex which is hexadecimal which is base sixteen and the important result that we had proved is that the octal and hexadecimal notations can be thought as short forms you know abbreviations or reduced representations of a binary representation so what do we do for example in base sixteen

we this group blocks of four binary numbers and ah represent them with one base sixteen number for example a number of this form right which is can be represented as this becomes one and this is actually eight plus three eleven which is d right so the instead of having eight digits you only have two digits then we represented negative integers we looked