To normalize the binary number [tex]\(111.01\)[/tex], we need to represent it in the form of [tex]\(1.xx \times 2^x\)[/tex].
Let's take the binary number [tex]\(111.01\)[/tex]:
1. Shift the binary point to the left until there is only one bit to its left:
```
111.01 → 1.1101
```
2. To keep the value equivalent after shifting the point, we have to multiply by [tex]\(2\)[/tex] raised to the number of places we shifted:
- We shifted the binary point 2 places to the left.
- So, we multiply by [tex]\(2^2\)[/tex].
Putting this together, we get:
[tex]\[
1.1101 \times 2^2
\][/tex]
Therefore, the normalized form of the mantissa [tex]\(111.01\)[/tex] is given by option D:
[tex]\[
\boxed{1.1101 \times 2^2}
\][/tex]
