NIMCET Floating Point Representation Previous Year Questions (PYQs)
A Place for Latest Exam wise Questions, Videos, Previous Year Papers,
Study Stuff for MCA Examinations
Study Stuff for MCA Examinations
Showing 5 questions
In
order to store floating numbers in computer using the normalized representation
and 32-bit single precision, the number of bits used for exponent and fraction
are __________, __________ respectively.
1
2
3
4
Solution
Consider the values A = 2.0 × 1030, B = -2.0 × 1030 C = 1.0. Assume, that the floating point numbers
are represented with 32 bits. What are the values of X and Y, when the following sequence of operations are executed on a computer?
X = A + B
Y = A + C
X = X + C
Y = Y + B
1
2
3
4
Solution
Suppose we have a 10-bit computer that uses 10-bit floating point computational unit (Float number uses IEEE floating-point arithmetic where a floating point number has 1 sign bit, 5 exponent bits, and 4 fraction bits). The representation for +∞ (plus infinity) is
1
2
3
4
Solution
10-bit Floating Point: +∞ Representation
Format: The 10-bit floating point is structured as follows:
- 1 bit for sign (S)
- 5 bits for exponent (E)
- 4 bits for fraction/mantissa (F)
IEEE Rule for +∞:
In IEEE floating-point format, +∞ is represented as:
- Sign bit (S): 0
- Exponent bits (E): all 1s →
11111 - Fraction bits (F): all 0s →
0000
✅ Final 10-bit Representation: 0111110000
The
range of the exponent E in the IEEE754 double precision (Binary 64) format is
_____
1
2
3
4
Solution
✅ IEEE 754 Double Precision Format:
The **exponent** field in the IEEE 754 double precision (Binary 64) format is 11 bits long and uses a **bias of 1023**.
✅ Step-by-Step Explanation:
- The exponent field has **11 bits**, which means it can represent values between **0 and 2047**.
- The exponent is stored in **biased form**: the stored value is the actual exponent + 1023.
- For **normalized numbers**, the exponent range is:
- Minimum exponent: \( 1 - 1023 = -1022 \)
- Maximum exponent: \( 2046 - 1023 = +1023 \)
- Special cases:
- **Exponent = 0**: Used for **denormalized numbers**.
- **Exponent = 2047**: Represents **infinity** or **NaN** (Not a Number).
✅ Final Answer:
The range of the exponent E in the IEEE 754 double precision (Binary 64) format is:
From -1022 to +1023 (for normalized numbers)
Floating point numbers in a computer are represented using a 10-bit mantissa (including a sign bit) a 7-bit exponent (including a sign bit). What is the approximate value of the maximum number, which can be represented? Assume that the mantissa is stored in the normalized form, that is, without leading zeroes.
1
2
3
4
Solution
7-bit exponent including sign → maximum exponent = $2^{6}-1 = 63$
Hence maximum representable value ≈ $2^{63}$.
NIMCET
Online Test Series, Information About Examination,
Syllabus, Notification
and More.
View More
NIMCET
Online Test Series, Information About Examination,
Syllabus, Notification
and More.
View More
Ask Your Question or Put Your Review.
