The Language of Bits Part-II

so now we have discussed about representing positive integers in our system which is actually very easy so let us now discuss how to represent negative integers in our system using zeros and ones so ah whats the problem what we want to do is that given a negative integers we want to assign a binary representation to it in terms of just in a zeros and ones so

consider a negative integer s assume that is binary form is x n ah to x one so this is the least significant bit and x n is the most significant bit and hence forth we will actually start counting from one not from zero so now we can also you know given this number over here which we are representing we can also expanded to represent an unsigned

unsigned means without a sign assumed to be positive number n so we can interpret this binary sequence here in two ways one is we can interpret it as an unsigned number so we will get n or we can represent it as a number with the sign and we will get s so the so what we need to do is we need to create a mapping ah from

the set of all the numbers with a sign which can include both positive numbers as well as negative numbers to a set of binary unsigned numbers called n so ah this mapping would essentially tell us how to represent a number be positive or negative using a set of binary bits so let the set of positive and negative numbers be called as and let each number irrespective

of its sign positive or negative be map through a sequence of binary numbers and we can alternatively interpret this number as a positive number and lets call this set as n if you find a mapping will be able to represent both positive as well as negative numbers using a binary representation for the positive numbers we already have some idea from a previous discussion