A7.3 Fixed point and floating point

Write two functions. - float_value(mantissa, exponent): mantissa is a string of 8 characters 0 or 1, a two's complement fixed point number with the binary point after the first bit (place values -1, ½, ¼ down to 1/128). exponent is a string of 4 characters 0 or 1, a two's complement integer from -8 to 7. It returns the value, mantissa × 2 to the power of exponent, as a float. - is_normalised(mantissa): returns True when the first two bits of the mantissa are different, otherwise False. The loop prints each line as 01101000 0011 = 6.5 normalised or 00011000 0101 = 6.0 not normalised, with the value exactly as Python prints the float.

# the two lines every program starts with: the commands, then the robot
from bugbot import *
connect()

def float_value(mantissa, exponent):
    return 0.0

def is_normalised(mantissa):
    return False

for mantissa, exponent in [("01101000", "0011"), ("10110000", "0010"), ("00011000", "0101"), ("11100000", "1111")]:
    word = "normalised" if is_normalised(mantissa) else "not normalised"
    print(mantissa, exponent, "=", float_value(mantissa, exponent), word)

The hint students can ask for: The mantissa's place values start at -1 and then halve: 1/2, 1/4, 1/8 and so on. The exponent is an ordinary two's complement integer with -8 as its first place value. The value is the mantissa multiplied by 2 to the power of the exponent. A normalised mantissa's first two bits are different.

A solution

# the two lines every program starts with: the commands, then the robot
from bugbot import *
connect()

def float_value(mantissa, exponent):
    m = -1.0 if mantissa[0] == "1" else 0.0
    place = 0.5
    for bit in mantissa[1:]:
        if bit == "1":
            m = m + place
        place = place / 2
    e = -8 if exponent[0] == "1" else 0
    e = e + int(exponent[1:], 2)
    return m * 2 ** e

def is_normalised(mantissa):
    return mantissa[0] != mantissa[1]

for mantissa, exponent in [("01101000", "0011"), ("10110000", "0010"), ("00011000", "0101"), ("11100000", "1111")]:
    word = "normalised" if is_normalised(mantissa) else "not normalised"
    print(mantissa, exponent, "=", float_value(mantissa, exponent), word)

Any program that meets the task's checks is marked correct in the simulator; this is one way, not the only way.