CP-2 Fixed & Floating Point · GATE 2027 Digital Logic

Phase 2 Checkpoint: 15 questions on fixed and floating point.

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15 questions · 22 marks · 45 minutes. Negative marking on MCQ only: −1/3 mark for a wrong 1-mark MCQ, −2/3 for a wrong 2-mark MCQ. No negative marking for MSQ or NAT; MSQ has no partial credit.

Q1NAT1 markFixed value

Unsigned 4.4 pattern 0110.0110: what real number?

Numerical answer: ________

Q2NAT2 marksFixed range

Unsigned fixed point with 5 integer bits and 3 fraction bits: what is the largest value?

Numerical answer: ________

Q3MCQ1 markFixed negative

−5.75 in signed 4.4 fixed point is:

(A) 1010.0100
(B) 0101.1100
(C) 1010.0011
(D) 1101.1100

Q4NAT2 marksRounding

With 4 fraction bits and rounding to nearest, what is the largest possible representation error? Give a decimal.

Numerical answer: ________

Q5NAT1 markField sizes

How many fraction (mantissa) bits does IEEE 754 double precision store?

Numerical answer: ________

Q6MCQ2 marksEncode

−0.375 in single precision (hex) is:

(A) BE40 0000
(B) BEC0 0000
(C) BF40 0000
(D) 3EC0 0000

Q7NAT2 marksDecode

What value does the single-precision pattern 0x3E20 0000 represent? Give a decimal.

Numerical answer: ________

Q8NAT1 markExponent

What is the exponent field (decimal) of −13.25 in single precision?

Numerical answer: ________

Q9MCQ1 markInexact

Which of these values is stored exactly in single precision?

(A) 1/3
(B) 0.2
(C) 0.15625
(D) 0.1

Q10MCQ1 markInfinity

The single-precision pattern 0xFF80 0000 represents:

(A) the most negative normal number
(B) NaN
(C) −0
(D) −∞

Q11NAT2 marksLargest

The largest single-precision normal number is (2 − 2⁻²³) × 2ᵏ. What is k?

Numerical answer: ________

Q12NAT2 marksGap

What is the gap between consecutive single-precision numbers in [1024, 2048)? Give a decimal.

Numerical answer: ________

Q13NAT2 marksHalf precision

IEEE half precision has 1 sign bit, 5 exponent bits and 10 fraction bits. What is its largest finite value?

Numerical answer: ________

Q14MCQ1 markAssociativity

In single precision, x = 2²⁴. Which is true?

(A) x + 1 overflows
(B) (x + 1) + 1 = x, but x + (1 + 1) = x + 2
(C) (x + 1) + 1 = x + (1 + 1)
(D) x + 1 = x + 2

Q15NAT1 markBias

A custom floating-point format has 6 exponent bits with IEEE-style bias. What is the bias?

Numerical answer: ________

✓Answer Vault

Answer Vault

Try the questions first. Open when you are ready to check.

Q1 Answer: 6.3751 mark

6 + 0.25 + 0.125.

Re-read: Lesson 2.1.1 — Fixed-point binary fractions: range, precision and rounding

Q2 Answer: 31.8752 marks

32 − 1/8.

Re-read: Lesson 2.1.1 — Fixed-point binary fractions: range, precision and rounding

Q3 Answer: (A)1 mark

2's complement of 0101.1100 as one 8-bit number.

(B) is wrong: +5.75.
(C) is wrong: 1's complement.
(D) is wrong: Sign-magnitude.

Re-read: Lesson 2.1.1 — Fixed-point binary fractions: range, precision and rounding

Q4 Answer: 0.031252 marks

Half of 1/16.

Re-read: Lesson 2.1.1 — Fixed-point binary fractions: range, precision and rounding

Q5 Answer: 521 mark

1 + 11 + 52 = 64.

Re-read: Lesson 2.1.2 — Floating point and IEEE 754: sign, biased exponent, mantissa

Q6 Answer: (B)2 marks

−0.011₂ = −1.1 × 2⁻²: S 1, E 125, F 1….

(A) is wrong: That is −0.1875 (exponent one too small).
(C) is wrong: That is −0.75.
(D) is wrong: Positive.

Re-read: Lesson 2.1.2 — Floating point and IEEE 754: sign, biased exponent, mantissa

Q7 Answer: 0.156252 marks

E = 124 → e = −3; 1.01₂ × 2⁻³.

Re-read: Lesson 2.1.2 — Floating point and IEEE 754: sign, biased exponent, mantissa

Q8 Answer: 1301 mark

1.10101 × 2³.

Re-read: Lesson 2.1.2 — Floating point and IEEE 754: sign, biased exponent, mantissa

Q9 Answer: (C)1 mark

5/32: the denominator is a power of 2.

(A) is wrong: Never ends in binary.
(B) is wrong: 1/5.
(D) is wrong: 1/10.

Re-read: Lesson 2.1.2 — Floating point and IEEE 754: sign, biased exponent, mantissa

Q10 Answer: (D)1 mark

S 1, E all 1s, F 0.

(A) is wrong: That has E = 254.
(B) is wrong: Needs F ≠ 0.
(C) is wrong: −0 is 0x8000 0000.