contents.m

Two functions, num2bin and bin2num are provided. num2bin takes a double and converts it to a binary

%contents
% There are times when it is instructive to see a binary string
% representation of a number. The function num2bin provides
% functionality for creating this representation. Another function
% bin2num reverses the operation. These scripts are useful in
% an elementary numerical analysis course. Both functions
% have been tested with MATLAB 5 or later.
%
% >x = pi;
% >s = num2bin(x)
% s =
% 
% +.11001001000011111101101010100010001000010110100011000*2^+2
% A 53 bit fraction is shown along with the scaling factor.
%
% The inverse operation is found in bin2num.
% >z = bin2num(s)
% z =
% 
%    3.14159265358979
% >z==x
% ans =
%      1
%
%Quantities of interest in numical analysis are eps, realmax, and realmin. The usual
%formatting in MATLAB doesn't show the fine structure.

% >z = num2bin(realmax)
% z =
% +.11111111111111111111111111111111111111111111111111111*2^+1024
%
%>z = num2bin(realmin)
% z =
% +.10000000000000000000000000000000000000000000000000000*2^-1021
%
% You can see denormalized numbers.
% >z = num2bin(.25*realmin)
% z =
% +.10000000000000000000000000000000000000000000000000000*2^-1023
%
%It is easy to see how eps behaves.
% >z = num2bin(eps)
% z =
% +.10000000000000000000000000000000000000000000000000000*2^-51
% >z = num2bin(1+eps)
% z =
% +.10000000000000000000000000000000000000000000000000001*2^+1
% >z = num2bin(1+eps*.5)
% z =
% +.10000000000000000000000000000000000000000000000000000*2^+1
%
% Herman Gollwitzer
% Mathematics and Computer Science
% Drexel University
% [e-mail]