consider the floating point system: f=[a=2,k−=−6,k+=6,t=4]the distance between 1 and its right neighbour (ε1 ) is: in matlab

In a floating-point system, ε, also known as machine epsilon, is defined as the smallest value that can be added to 1.0 to obtain a value different from 1.0 in the system. The value of ε depends on the number of bits used to represent the floating-point values and the internal representation of the system.

Given the floating-point system f=[a=2,k−=−6,k+=6,t=4], the distance between 1 and its right neighbor (ε1) can be calculated using the formula:

main.m
ε1 = a^(k-1)
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Substituting the given values in the formula:

main.m
ε1 = 2^(-5)  % Since k-1 = -6-1 = -5
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So the value of ε1 in the given floating-point system is 0.03125 (decimal).

In Matlab, you can calculate ε1 using the above formula as follows:

main.m
a = 2;
k_minus = -6;
epsilon_1 = a^(k_minus + 1)
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This will output 0.03125 as the value of ε1.