Problem 8:

Add the following numbers 0.5₍₁₀₎ and -0.4375₍₁₀₎ using the binary algorithm.

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₎