Number Systems · Digital Logic · GATE CSE
Marks 1
The number -6 can be represented as 1010 in 4-bit 2's complement representation. Which of the following is/are CORRECT 2's complement representation(s) of $-6$ ?
The format of a single-precision floating-point number as per the IEEE 754 standard is:
| Sign (1 bit) | Exponent (8 bits) | Mantissa (23 bits) |
|---|
Choose the largest floating-point number among the following options.
Consider a system that uses 5 bits for representing signed integers in 2’s complement format. In this system, two integers A and B are represented as A=01010 and B=11010. Which one of the following operations will result in either an arithmetic overflow or an arithmetic underflow?
A particular number is written as 132 in radix-4 representation. The same number in radix-5 representation is ____________.
Let R1 and R2 be two 4-bit registers that store numbers in 2's complement form. For the operation R1 + R2, which one of the following values of R1 and R2 gives an arithmetic overflow?
The format of the single-precision floating-point representation of a real number as per the IEEE 754 standard is as follows:
|
sign |
exponent |
mantissa |
Which one of the following choices is correct with respect to the smallest normalized positive number represented using the standard?
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 ______
Then $$X −Y$$ is ____________.
$${{312} \over {20}} = 13.1$$
Marks 2
Three floating point numbers $X, Y$, and $Z$ are stored in three registers $R_X, R_Y$, and $R_Z$, respectively in IEEE 754 single precision format as given below in hexadecimal:
$$R_X=0 \times C 1100000, R_Y=0 \times 40 C 00000, \text { and } R_Z=0 \times 41400000$$
Which of the following option(s) is/are CORRECT?
Which of the following is/are EQUAL to 224 in radix-5 (i.e., base-5) notation?
Consider the IEEE-754 single precision floating point numbers P=0xC1800000 and Q=0x3F5C2EF4.
Which one of the following corresponds to the product of these numbers (i.e., P $$\times$$ Q), represented in the IEEE-754 single precision format?
Consider three floating point numbers A, B and C stored in registers RA, RB and RC, respectively as per IEEE-754 single precision floating point format. The 32-bit content stored in these registers (in hexadecimal form) are as follows.
Which one of the following is FALSE?
If R3 = $${{R1} \over {R2}}$$, what is the value stored in R3?
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?
The value of the radix' $$r$$ is:
$${16^3} \times 9 + {16^2} \times 7 + 16 \times 5 + 3$$
The number of $$1's$$ in the unsigned binary representation of the number is _______.