What is the minimum number for N to calculate the value of ln x for x = 4.5 exactly as a half precision number? Use the function decimal2binary to answer this question.

MY FUNCTION

function [m,p,r] = decimal2binary(x,N)

%Input %x: decimal number to translate %N: number of mantissa bits to use. %output %m:vector of N mantissa bits %p: decimal exponent of the binary floating number %r: remainder

m = zeros(N,1); p = floor(log(x)/log(2));

n = p;

%calculate the remainder x taking the hidden bit into account x = x-2^n;

%loop over all requested mantissa bits for i = 1:N n = p-i; %working exponent of the i-th bit if 2^n <= x m(i) = 1; %set bit to 1 x = x-2^n; % update the remainder end end

%remainder r = x;

end