Computer Arithmetic Part-I

[Music] la [Music] well welcome to chapter 7 this is a chapter on computer arithmetic we shall use all the knowledge that we have gained in designing digital logic all the knowledge that we gained in Chapter 2 the language of bits to design circuits in this chapter to implement adders multipliers and dividers so this is uh chapter 7 of the

book computer organization and architecture published by mcro in 2015 so we'll have we have these six parts in this chapter uh we have addition multiplication and division so these are integer addition multiplication and division and then we have floating Point addition multiplication and division so the entire chapter is broken down into six

sections so let's take a look at the simplest problem which is to add two one bit numbers A and B so if we add two one bit numbers is uh what is it that we can get the largest number that we can get will actually require two bits so let's see how and

why if we add 0 and zero so let's assume the output is two bits so the output is 0 0 if you add 1 and Zer the output is 0 1 similarly if you add 0 and 1 the output is 01 and if you add 1 and 1 uh the output is 1 Z so 1 so 1 + 1 is

two and the representation of two is 1 and zero so what we see is that for the first three results one bit is sufficient for the last result we need two bits so pretty much we can say that we add two one bit numbers the final result can take two bits so it's better

if you allocate two bits so the least significant bit of the result of so it's a two bit result right so the least significant bit which is let's say this bit is known as uh the sum and the most significant bit is known as the carry so we shall see why if you add 0