Question

Consider the following statements: \[ \begin{aligned} (i) &\ \text{Perform addition/subtraction on the mantissas} (ii) &\ \text{Set the exponent of the result} (iii) &\ \text{Choose the number with the smaller exponent and shift its mantissa} (iv) &\ \text{Normalize the result} \end{aligned} \] Find the correct add/subtract rule sequence.

• A. (i), (iii), (ii), (iv)
• B. (iii), (i), (iv), (ii)
• C. (i), (ii), (iv), (iii)
• D. (iii), (ii), (i), (iv)

Hint:

Floating-point addition rule: \[ \text{Align Exponents} \rightarrow \text{Add/Subtract Mantissas} \rightarrow \text{Normalize} \rightarrow \text{Adjust Exponent} \] Always remember: exponent alignment comes first.

Answer 1

The Correct Option is B

Concept: Floating-point arithmetic is used to represent very large and very small numbers in computers. A floating-point number consists of two parts: \[ \text{Number} = \text{Mantissa} \times \text{Base}^{\text{Exponent}} \] Before two floating-point numbers can be added or subtracted, their exponents must be made equal.

Step 1: Align the exponents.
When two floating-point numbers have different exponents, the mantissa corresponding to the smaller exponent is shifted until both exponents become equal. Therefore the first operation is: \[ (iii) \]

Step 2: Perform mantissa addition/subtraction.
After alignment of exponents, the mantissas are added or subtracted. \[ (i) \]

Step 3: Normalize the result.
The obtained result may not be in normalized form. Hence normalization is performed. \[ (iv) \]

Step 4: Determine the final exponent.
After normalization, the exponent of the result is adjusted accordingly. \[ (ii) \]

Step 5: Write the correct sequence.
\[ (iii)\rightarrow(i)\rightarrow(iv)\rightarrow(ii) \] Thus, \[ \boxed{(iii),(i),(iv),(ii)} \] Hence option (B) is correct.