Question

Consider a computer which stores a floating point number in a 9-bits memory. Positive sign is stored as zero, and negative is 1 . First bit indicates the sign of the number, second bit indicates the sign of the exponent, next three bit indicates the exponent, and the last four bits indicate the magnitude of the mantissa. Find the representation of -17.433725 number in this computer memory. (20p)

Answer 1

To represent -17.433725 in a 9-bit memory, the binary representation would be 1101101000.

Step-by-step explanation:

To represent the number -17.433725 in a 9-bit memory, we can follow the given format. Positive sign is stored as zero, so the sign bit will be 1. The second bit indicates the sign of the exponent, so since the exponent will be negative, the second bit will be 1 as well. The next three bits indicate the exponent, and for -17.433725, the exponent can be represented as -3 in binary, which is 101.

The last four bits indicate the magnitude of the mantissa. To find the magnitude, we can convert the absolute value of -17.433725 to binary. The binary representation of the magnitude will be 1000.

Putting it all together, the representation of -17.433725 in this computer memory would be 1101101000.