Question

A floating-point number is said to be normalized, if the MSB (Most Significant Bit) of the mantissa is ______.

• A. -1
• B. 0
• C. 1
• D. 2

Hint:

In standard binary floating-point, normalization involves a leading '1'. '-1' indicates a non-standard format.

Answer 1

The Correct Option is A

Understanding the concept of normalized floating-point numbers.
A floating-point number is said to be normalized when the Most Significant Bit (MSB) of the mantissa is 1. This ensures that the number is represented in its most compact and efficient form.
In normalized form, the mantissa (or significand) is always adjusted so that its leading bit is 1. This is the standard format for floating-point numbers, which allows the system to maximize precision by not using unnecessary leading zeros.
For example, in IEEE 754 standard for binary floating-point numbers, the normalized representation of a number is such that the leading digit of the mantissa is always 1, which simplifies the encoding of numbers. \[ \text{Normalized Floating Point: } \text{MSB of Mantissa} = 1 \]