consider the floating point system: f=[a=2,k−=−6,k+=6,t=4]the smallest positive, normalized element (ε0 ) is: in matlab

In a floating point system, the smallest positive, normalized element (epsilon) can be calculated using the formula:

epsilon = base^(minimum_exponent - significant_digits)

where,

base = radix of the floating point system (for binary system, base is 2) minimum_exponent = value of k- in given floating point system significant_digits = number of bits in mantissa fraction (t in given system)

Substituting these values in the formula given above for the given system:

epsilon = 2^(-6-4) = 2^(-10) = 0.0009765625

Therefore, the smallest positive, normalized element (epsilon) would be 0.0009765625 in the given floating point system.

To calculate this in matlab code, we can do:

main.m
base = 2; 
minimum_exponent = -6; 
significant_digits = 4; 

epsilon = base^(minimum_exponent - significant_digits)
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This will give the output as:

main.m
epsilon = 0.0009765625
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