The representation of a floating point binary number +1001.11 in 8 bit fraction and 6 bit exponent format is

✅ Given:

The floating-point binary number is \( +1001.11_2 \).

We need to convert it into an 8-bit fraction and a 6-bit exponent format.

✅ Step 1: Normalize the Binary Number

We start by normalizing the binary number into scientific notation of the form:

\( 1.xxxx \times 2^n \)

Converting \( 1001.11_2 \) into scientific notation gives:

\( 1001.11_2 = 1.00111_2 \times 2^3 \)

The exponent is \( 3 \) (because the binary point is shifted 3 places to the left).

✅ Step 2: Convert the Exponent to Binary

The exponent is \( 3 \) in decimal. To represent this in binary using 6 bits, we get:

\( \text{Exponent} = 000100_2 \)

✅ Step 3: Convert the Fraction to 8 Bits

The fractional part of the normalized binary number is \( 00111 \). We need to extend it to 8 bits:

\( \text{Fraction} = 01001110_2 \)

✅ Final Answer:

The floating-point binary number \( +1001.11_2 \) in 8-bit fraction and 6-bit exponent format is:

Exponent: \( 000100_2 \), Fraction: \( 01001110_2 \)