We read your photo as:

Separate the mantissa and exponent.

Mathematics

ScanSolve AI Answer

Step-by-step solution

3 steps

b) i) Show how this number can be normalized.

  1. Separate the mantissa and exponent.

    The given floating-point binary number is 11101011.
    It is stored using 5 bits for the mantissa and 3 bits for the exponent.
    Mantissa: 11101211101_2
    Exponent: 0112011_2

  2. Convert the mantissa to its denary (decimal) equivalent.

    The mantissa 11101211101_2 is in 2's complement form. The binary point is assumed after the first bit (sign bit).
    So, the mantissa is 1.110121.1101_2.
    Since the MSB is 1, it's a negative number.
    Value =−1⋅20+1⋅2−1+1⋅2−2+0⋅2−3+1⋅2−4= -1 \cdot 2^0 + 1 \cdot 2^{-1} + 1 \cdot 2^{-2} + 0 \cdot 2^{-3} + 1 \cdot 2^{-4}
    Value =−1+0.5+0.25+0+0.0625=−1+0.8125=−0.187510= -1 + 0.5 + 0.25 + 0 + 0.0625 = -1 + 0.8125 = -0.1875_{10}.

  3. Convert the exponent to its denary equivalent.

    The exponent 0112011_2 is in 2's complement form.

Was this helpful?

Still stuck on this one?

Ask a follow-up, and the answer starts from this question.

Got a different question?Ask your own question
Handwritten step-by-step solution preview

Handwritten Step-by-Step Solution

Get this as a handwritten image on WhatsApp — like a tutor wrote it for you.

Try on WhatsApp