Lecture 3
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MEEN 357 Homework Solution
1
Lecture-03-Homework-Solution-2009.doc
RMB
1.
Convert the following 64 bit number to a real number:
1
10010001111
1100001101010000000010000000000000000000000000000000
S
Exp
M
=
=
=
Solution:
There are a lot of different ways to do the arithmetic, including by hand.
Below is script for an mfile that will make MATLAB do the calculation.
%calculates number from 64 bit IEEE binary number.
Not
%fancy.
...Uses
%notation in 357 notes.
clc
clear
all
format
long
S=1
%Calculation of E
%You are given
Exp=[1 0 0 1 0 0 0 1 1 1 1]
%Next build the formula (3.41)for E
K=10:-1:0;
N=2.^(K);
E=N*Exp'
%Next build the formula (3.45) for f
%Build a matrix for all of the given and leading zeros in M
Q=zeros(1,31)
%Concatenate Q with the other given entries in M
M=[1,1,0,0,0,0,1,1,0,1,0,1,0,0,0,0,0,0,0,0,1,Q]
K=1:52;
L=1./(2.^(K));
f=M*L';
%calculation of v from the table on page 17 of the notes
%for Lecture 3
format
long
e
v=(-1)^S*(1+f)*2^(E-1023)
%While not necessary, you can display your results as