Computer Arithmetic Part-V

Welcome back. So, let's take a look at floating-point addition. So, we'll take a look at all three floating-point addition, multiplication, and division. So, let's start with addition. Addition and multiplication are done almost similarly. Division is however different and is very interesting. All right. So, let's uh quickly go back to chapter two and uh quickly uh do a revision of how

floating-point numbers are stored. So, we'll use 32-bit uh 32-bit number system as the running example. But, you know, the same results hold for 64-bit. So, I'll not uh you know, in the cost of uh you know, not repeating uh you know, repeating the same thing rather, I'll not repeat it. So, uh in a 32-bit number system, we uh

share one uh I'm sorry, we store one bit. The most significant bit is the sign bit. So, uh so, any number that has a normalized form, so, the normalized form basically says uh that we uh take this number minus one. And to the power S, so, if S is zero, the sign bit is zero means that this is

one. Otherwise, if the sign bit is one, means that minus one to the power S is minus one. So, it's the number is negative. Then, uh we store a significant. So, the significant is of the form 1. a sequence of 23 zeros or ones. So, the significant is less than greater than equal to one or rather

one is less than equal to P and is less than two. Then we have two times E minus bias where E is the real uh So, it's the E is the exponent that is stored and uh bias is 127.

So, for example, if you want to represent a number of the form uh let's say 1.5. Okay, let me go maybe here. Uh let's say we want to represent a number of the form 1.5. So, 1.5 in base 10 would translate to 1.1 in base two. So, in this case the sign bit is zero.