To solve the problem of identifying the normalized form of the mantissa in the binary number 111.01, we need to follow these steps:
1. Understand what normalization means: In binary, normalization refers to expressing the number in the form [tex]\( M \times 2^E \)[/tex] where [tex]\( M \)[/tex] (the mantissa) has exactly one non-zero digit to the left of the decimal point.
2. Convert 111.01 to normalized form:
- We start with 111.01 in binary.
- To normalize it, we shift the decimal point such that there is one non-zero digit to its left.
- By shifting the decimal point two positions to the left, we obtain [tex]\( 1.1101 \)[/tex]. This leaves us with:
[tex]\[
1.1101 \times 2^2
\][/tex]
- Here, [tex]\( 1.1101 \)[/tex] is the mantissa and [tex]\( 2 \)[/tex] is the exponent, representing the shift of the decimal point.
3. Check against the given options:
- [tex]\( A. 1.1101 \times 2^2 \)[/tex]
- [tex]\( B. 11.101 \times 2^1 \)[/tex]
- [tex]\( C. 0.11101 \times 2^3 \)[/tex]
- [tex]\( D. 1110.1 \times 2^{-1} \)[/tex]
The normalization of 111.01 is [tex]\( 1.1101 \times 2^2 \)[/tex].
Therefore, the correct answer is:
[tex]\[
\boxed{1}
\][/tex]
The normalized form of the mantissa in 111.01 is [tex]\( 1.1101 \times 2^2 \)[/tex].
