Question

In floating-point representation, the part that represents a signed and fixed-point number, and the position of the decimal point are called ______ and ______.

• A. Mantissa, Exponent
• B. Exponent, Mantissa
• C. Float, Exponent
• D. Mantissa, Float

Hint:

Visualize a floating-point number in scientific notation (e.g., \( 1.23 \times 10^4 \)). Here, 1.23 is related to the mantissa, and 4 is related to the exponent.

Answer 1

The Correct Option is A

Step 1: Understand the concept of Floating-Point Representation.
Floating-point representation is a way of approximating real numbers in a computer system. It is designed to handle a wide range of values, both very large and very small, using a fixed number of bits. Step 2: Identify the key components of a floating-point number.
A typical floating-point number consists of three main parts:
a. Sign bit: Indicates whether the number is positive or negative.
b. Exponent: Determines the magnitude or scale of the number by specifying the power of the base (usually 2). This effectively controls the position of the radix point (decimal point in base 10, binary point in base 2).
c. Mantissa (or Significand): Represents the significant digits of the number. It is often normalized to have a single non-zero digit before the radix point (in its conceptual form before encoding).
Step 3: Relate the question's description to these components.
The question mentions "the part that represents a signed and fixed-point number" and "the position of the decimal point". Step 4: Match the description to the correct terms.
The mantissa is the part that holds the significant digits and is treated as a fixed-point number (though often normalized). The sign of the floating-point number is associated with the mantissa.
The exponent determines the scale factor (a power of the base) that is multiplied by the mantissa. This scaling factor effectively shifts the position of the radix point, allowing the number to "float".
Step 5: Evaluate the given options.
(1) Mantissa, Exponent: This correctly identifies the mantissa as the signed fixed-point part and the exponent as controlling the decimal point's position.
(2) Exponent, Mantissa: This reverses the correct order.
(3) Float, Exponent: "Float" is a data type that uses floating-point representation, not a component of the representation itself.
(4) Mantissa, Float: Similar to option (3), "float" is a data type, not a component.
Step 6: Conclude the correct answer.
The part representing the signed fixed-point number is the mantissa, and the part indicating the position of the decimal point is the exponent.