Select the correct answer.

Identify the normalized form of the mantissa in 111.01.

A. [tex]1110.1 \times 2^{-1}[/tex]
B. [tex]0.11101 \times 2^3[/tex]
C. [tex]11.101 \times 2^1[/tex]
D. [tex]1.1101 \times 2^2[/tex]



Answer :

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]