1
GATE CSE 2021 Set 1
Numerical
+2
-0.67

Consider the following representation of a number in IEEE 754 single-precision floating point format with a bias of 127.

S: 1 E:   10000001    F : 11110000000000000000000

Here S, E and F denote the sign, exponent and fraction components of the floating point representation.

The decimal value corresponding to the above representation (rounded to 2 decimal places) is ______

2
GATE CSE 2020
MCQ (Single Correct Answer)
+2
-0.67
Consider three registers R1, R2 and R3 that store numbers in IEEE-754 single precision floating point format. Assume that R1 and R2 contain the values (in hexadecimal notation) 0x42200000 and 0xC1200000, respectively.
If R3 = $${{R1} \over {R2}}$$, what is the value stored in R3?
A
0x40800000
B
0x40800000
C
0xC8500000
D
0xC0800000
3
GATE CSE 2018
MCQ (Single Correct Answer)
+2
-0.6
Consider the unsigned $$8$$-bit fixed point binary number representation below $${b_7}\,\,{b_6}\,\,{b_5}\,\,{b_4}\,\,{b_3}\,\,.\,\,{b_2}\,\,{b_1}\,\,{b_0}$$\$
where the position of the binary point is between $${b_3}$$ and $${b_2}$$. Assume $${b_7}$$ is the most significant bit. Some of the decimal numbers listed below cannot be represented exactly in the above representation:
$$\,\,\,\,\,\,\,\,\,\,\,\,\,$$ $$(i)$$ $$31.500$$ $$\,\,\,\,\,\,\,\,\,\,\,\,\,$$ $$(ii)$$ $$0.875$$ $$\,\,\,\,\,\,\,\,\,\,\,\,\,$$ $$(iii)$$ $$12.100$$ $$\,\,\,\,\,\,\,\,\,\,\,\,\,$$ (iv) $$3.001$$

Which one of the following statements is true?

A
None of $$(i), (ii), (iii), (iv)$$ can be exactly represented
B
Only $$(ii)$$ cannot be exactly represented
C
Only $$(iii)$$ and $$(iv)$$ cannot be exactly represented
D
Only $$(i)$$ and $$(ii)$$ cannot be exactly represented
4
GATE CSE 2015 Set 3
Numerical
+2
-0
Consider the equation $${\left( {43} \right)_x} = {\left( {y3} \right)_8}$$ where $$x$$ and $$y$$ are unknown. The number of possible solutions is ______________