(Solved Homework): Start with x = 1.0 and keep dividing it by 2 until you get 0.0. If n + 1 is the number of such divisions, then 1/2^n is the smallest nu…

In Python

Start with x = 1.0 and keep dividing it by 2 until you get 0.0. If n + 1 is the number of such divisions, then 1/2^n is the smallest number representable in the floating point format in the programming environment of your choice. Similarly, if at the stage m + 1, 1.0 + x 1.0, then 1.0 + 1/2^m is the floating point number closest to 1.0. Now start doubling 1.0 until you get +INF (or NaN) at some stage, N + 1: then 2^N (2 – 1/2^m) is the largest floating point number. Obtain m, n, and N. Discuss your findings: deduce the numbers of bits that are used in your environment for the exponent and significant of the floating point numbers.

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(Solved Homework): Start with x = 1.0 and keep dividing it by 2 until you get 0.0. If n + 1 is the number of such divisions, then 1/2^n is the smallest nu…
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# test 1
x = 1.0
result = x / 2
iterator = 0

while result != 0.0:
iterator += 1
result /= 2

print “n ==”, iterator-1

# test 2
x = 1.0
result = x / 2
iterator = 0

while 1.0 + result != 1.0:
iterator += 1
result /= 2

print “m ==”, iterator-1

# test 3
x = 1.0
result = x * 2
iterator = 0

while result != float(‘inf’):
iterator += 1
result *= 2

print “N ==”, iterator-1

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