To identify the normalized form of the mantissa in the binary number 111.01, we need to express it in a scientific notation form where the mantissa is a binary fraction starting with 1 (i.e., 1.xxxxx) and followed by a power of 2.
Here is the step-by-step process to normalize 111.01:
1. Original Binary Number: The given binary number is 111.01.
2. Normalization: To normalize the number, we need to move the decimal point to the left until we have exactly one digit before the decimal point.
- Starting number: 111.01
- Move the decimal point 1 place to the left: 11.101 × 2¹
- Move the decimal point another place to the left: 1.1101 × 2²
3. Resulting Normalized Form: After moving the decimal point, we get the normalized form as 1.1101 × 2². Here, the mantissa is now in the form 1.xxxxx, and the exponent indicates how many places the decimal point was moved.
Therefore, the correct answer is:
D. [tex]\( 1.1101 \times 2^2 \)[/tex]
