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def ieee(f, word=32):
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"""Generate the binary string representing a floating-point value in IEEE754 code."""
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f = float(f)
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if word not in (16, 32, 64, 128):
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raise ValueError("IEEE754 is defined for 16, 32, 64 and 128 bit words.")
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exp_bin = range({16:5, 32:8, 64:11, 128:15}[word])
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frac_bin = range(word - len(exp_bin) - 1)
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# Sign.
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sign_bin = [int(f < 0)]
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f = abs(f)
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# Find exponent (adding the bias).
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bias = 2**(len(exp_bin)-1) -1
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exponent = bias
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while f >= 2:
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exponent += 1
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f /= 2
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while f < 1 and exponent > 0:
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exponent -= 1
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f *= 2
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if not 0 <= exponent < 2*(bias+1):
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raise ValueError("Exponent overflow: Absolute exponent must be smaller than %d." % (bias + 1))
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# Encode exponent in binary.
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for i in exp_bin[::-1]:
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exp_bin[i] = int(exponent % 2)
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exponent /= 2
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# Remove the leading 1 bit.
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f -= 1
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for i in frac_bin:
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f *= 2
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frac_bin[i] = int(f >= 1)
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f -= frac_bin[i]
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# Join the binary string components together.
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return "".join(map(str, sign_bin + exp_bin + frac_bin))
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def ieee_decode(binary):
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"""Decode a binary string representing a floating-point value in IEEE754 code."""
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# Determine the word size of the binary.
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word = len(binary)
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if word not in (16, 32, 64, 128):
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raise ValueError("IEEE754 is defined for 16, 32, 64 and 128 bit words.")
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# Determine the length of the exponent.
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e = {16:5, 32:8, 64:11, 128:15}[word]
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# Turn the binary string into a bit-list.
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binary = [int(c) for c in binary]
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# Split the components.
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sign = -2 * binary[0] + 1
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exp_bin = binary[1:1+e]
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frac_bin = binary[1+e:]
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# Decode the exponent.
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bias = 2**(e-1) - 1
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exponent = -bias
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c = 1
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for i in exp_bin[::-1]:
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exponent += i * c
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c *= 2
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# Decode the fraction.
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f = float(2**exponent)
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power = f
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for i in frac_bin:
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power *= 0.5
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f += i * power
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return sign * f
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if __name__ == "__main__":
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val = ieee(24.)
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val
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print val[:16]
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print val[0], val[1], val[2]
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val_in_int = int(val[:16], 2)
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print val_in_int
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print hex( val_in_int )
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