Consider the values:
\( A = 2.0 \times 10^{30} \)
\( B = -2.0 \times 10^{30} \)
\( C = 1.0 \)
Assume that floating-point numbers are represented with 32 bits. What are the values of \( X \) and \( Y \) after executing the following sequence of operations on a computer?
1. \( X = A + B \)
2. \( Y = A + C \)
3. \( X = X + C \)
4. \( Y = Y + B \)
- \( A = 2.0 \times 10^{30} \)
- \( B = -2.0 \times 10^{30} \)
- \( C = 1.0 \)
- 32-bit floating-point representation
Step-by-step Calculation:
1. Compute \( X \)
\[
X = A + B = (2.0 \times 10^{30}) + (-2.0 \times 10^{30}) = 0.0
\]
(Exact cancellation due to floating-point precision)
2. Compute \( Y \)
\[
Y = A + C = (2.0 \times 10^{30}) + 1.0 \approx 2.0 \times 10^{30}
\]
(Since \( C \) is much smaller, it is ignored due to floating-point precision)
3. Compute \( X = X + C \)
\[
X = 0.0 + 1.0 = 1.0
\]
4. Compute \( Y = Y + B \)
\[
Y = (2.0 \times 10^{30}) + (-2.0 \times 10^{30}) = 0.0
\]
(Exact cancellation)
Final Values:
- \( X = 1.0 \), \( Y = 0.0 \)
- Correct Answer: B (X = 1.0, Y = 0.0)
Reinforce your conceptual grasp with related questions from NIMCET 2014:
Take timed full-length mock tests with authentic question distributions, negative marking (+12/-3 in Math), and instant All India Rank calculation.
Start Free Mock Test Series →