Question

One of the following FP numbers is normalized:

A) 1101.11x2⁻¹
B) 1.1000111x2⁻¹
C) 0.110111x2⁻¹
D) 1101.000X2⁻⁶

Answer 1

The question asks which FP number is normalized, and the answer is option B) 1.1000111x2^-1 because it's the only option with a single non-zero digit before the decimal point in binary format.

Step-by-step explanation:

The question is asking which of the given floating-point (FP) numbers is normalized. A normalized FP number has a single non-zero digit before the decimal point. The exponent adjusts to account for the position of the decimal. In binary, a normalized number will start with 1. Considering the options, the only FP number that adheres to this format is B) 1.1000111x2-1.

• A) 1101.11x2-1 is not normalized because it starts with more than one digit before the decimal point.
• C) 0.110111x2-1 is not normalized because there is no leading digit before the decimal point.
• D) 1101.000X2-6 is also not normalized for the same reason as option A.

In scientific notation, the requirement is similar—the coefficient must be between 1 and 10, and the exponent adjusts accordingly.