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GATE 2022: Digital Logic Quiz-9

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Question 1

Consider the given 8 bit explicit normalized mantissa used for a floating data representation.

a₁ a₂ a₃ a₄ a₅ a₆ a₇ a₈

The difference value (in decimals) between maximum and minimum mantissa is ______.[round off to 5 decimal places]

Question 2

Consider the following hypothetical floating-point format.

The bias value in the floating-point format when the format uses excess code form is ________.

Question 3

Consider the following format of 32 bit floating point number:

(S) Sign: 1 bit
(E) Exponent: 8 bits
(M) Mantissa: 23 bits
The mantissa is normalized and has an implied “1” on the left of the point. Normalized form of mantissa is 1.M The exponent is formatted using excess-127 notation, with an implied base of 2. What will be the decimal value of the following 32 bit floating point number stored in above mentioned format?
1100000111111011000000000000000

Question 4

Consider the following floating point format:

The exponent is formatted using excess 16 notation with an implied base of 2. If the contents are:
Sign: 0
Exponent: 10111
Mantissa: 1100100000
What is the exponent value expressed by the above format?

Question 5

Consider the following values, using the IEEE 754 single precision floating-point format. What is
the equivalent value as a decimal number?

0101 1100 1010 0100 0100 0000 0000 0000

Question 6

Consider a modified 8-bit floating point representation in which 1-bit for sign, 3-bit for exponent and 4-bit for significant. What will be representation for decimal value –12?

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GATE & PSU CS Digital Logic

Aug 9GATE & PSU CS