ieee754.py

"""
This program demonstrates how to convert
floating-point numbers to IEEE 754 standard.

Set the "data_type" variable at the beginning
to either "double" or "float" to test how the
numbers are arranged differently under each type.

"""

data_type = "double"
exponent_length = 0
significand_lenth = 0

if data_type == "float":
    exponent_length = 8
    significand_lenth = 23

if data_type == "double":
    exponent_length = 11
    significand_lenth = 52

exponent_bais = 2**(exponent_length - 1) - 1

value = float(input("Enter a value: "))

"""
------------------------------------------------
    Part 1: Determine the sign.
------------------------------------------------
"""
print()
print("Determine the sign bit.")

sign_bit = "0"
if value < 0:
    sign_bit = "1"
    value = value * -1

print("Sign:", sign_bit)

"""
------------------------------------------------
    Part 2: Convert the number to binary.
------------------------------------------------
"""
print()
print("Convert the absolute value of our number to binary.")

whole_part = int(value)
fractional_part = value - whole_part

whole_str = ""
while whole_part > 0:
    whole_str = str(whole_part % 2) + whole_str
    whole_part = int(whole_part / 2)

if whole_str == "":
    whole_str = "0"

fractional_str = ""
while fractional_part > 0:
    fractional_str = fractional_str + str(int(fractional_part * 2))
    fractional_part *= 2
    fractional_part -= int(fractional_part)

if fractional_str == "":
    fractional_str = "0"

print("Binary: ", whole_str, ".", fractional_str)

"""
------------------------------------------------
    Part 3: Normalize.
------------------------------------------------
"""
print()
print("Convert the binary to a number which is 1.xxx * 2 ^ N:")

value_exponent = 0

while len(whole_str) > 1:
    fractional_str = whole_str[-1] + fractional_str
    whole_str = whole_str[:-1]
    value_exponent += 1

whole = int(whole_str)

while whole == 0 and int(fractional_str) > 0:
    whole = int(fractional_str[0])
    fractional_str = fractional_str[1:]
    value_exponent -= 1

if fractional_str == "":
    fractional_str = "0"

print("New Binary: ", whole, ".", fractional_str, "* 2 ^", value_exponent)
print()
print("----")
print("At this point, the whole part of the binary should be 1. It is no longer used.")
print("----")

"""
------------------------------------------------
    Part 4: Add the exponent bias.
------------------------------------------------
"""
print()
print("Add the exponent_bais (", exponent_bais, ") to the exponent.")
value_exponent += exponent_bais

print("New exponent: ", value_exponent)

"""
------------------------------------------------
    Part 5: Build the exponent string.
------------------------------------------------
"""
print()
print("Build exponent string.")

exponent_str = ""
for i in range(exponent_length):
    exponent_str = str(value_exponent % 2) + exponent_str
    value_exponent = int(value_exponent / 2)

print("Exponent string: ", exponent_str)

"""
------------------------------------------------
    Part 6: Build the significand.
------------------------------------------------
"""
print()
print("Build significand string.")

significand_str = fractional_str[:significand_lenth] + "0" * (significand_lenth - len(fractional_str[:significand_lenth]))

print("Significand:", significand_str)

"""
------------------------------------------------
    Part 7: Put all of the parts together.
------------------------------------------------
"""
print()
print("Finally, build the binary value.")
binary = sign_bit + exponent_str + significand_str
print("Binary:", binary)
print("Binary Length:", len(binary), "bits")