# Solution:

Step 1: Transform the numbers into binary:

0.5_{(10)} = 1.00_{ (2)} x 2^{-1} and -0.4375_{(10)} = -0.0111_{(2)} = -1.110_{(2)} x 2^{-2}

Step 2: Adjust the significant so that the exponents match.

-1.110_{(2)} x 2^{-2} = - 0.111_{(2)} x 2^{-1}

Step 3: Add the significands

1.00_{ (2)} x 2^{-1 }+ (- 0.111_{(2)} x 2^{-1}) = (1.00 – 0.111)x2^{-1} = 0.001_{(2)} x 2^{-1}^{}

Step 4: Normalize result and check for overflow/underflow

0.001_{(2)} x 2^{-1} = 1.000_{(2)} x 2^{-4}.

Step 5: Round and renormalize if necessary

1.000_{(2)} x 2^{-4}, no change necessary

Therefore, the finals answer is 1.000_{(2)} x 2^{-4} = 0.0625_{(10)}