HW10: done 2.4

Homework 10/assignment10.tex

@@ -1,5 +1,5 @@
 \documentclass[12pt]{article}
-\title{Assignment 10}
+\title{Computer Architecture -- Assignment 10}
 \author{Claudio Maggioni \and Tommaso Rodolfo Masera}
 \date{}
 
@@ -116,4 +116,17 @@ $1010011010.01000000000000\ =\ 2^9\ +\ 2^7\ +\ 2^4\ +\ 2^3\ +\ 2^1 +\ 2^{-2}\ =\
 
 \subsection{Exercise 2.4}
 
+In order to compute the number of IEEE 754 single-precision floating point numbers between 0 and 1 (both included), we first consider
+a constant positive ($= 1$) sign bit (and therefore we do not count it in our calculation of possible permutations).
+
+Then we count the number of denormalized numbers (including 0), which is: $2^{23} = 8388608$.
+
+After that, we count the number of valid from $2^{126}$ to $2^{1}$ included, which is 126. All these exponents will generate
+a number $< 1$ even with the highest possible mantissa. Then, we compute the number of numbers with these exponents, equal to:
+$126 * 2^{23} = 1056964608$.
+
+Finally, we consider the number 1 itself (0x3f800000) and we sum all the combinations: $8388608 + 1056964608 + 1 = 1065353217$
+
+Therefore, there are 1065353217 IEEE 754 single-precision floating point numbers between 0 and 1 (both included).
+
 \end{document}