GATE CS Number Representations (Fixed and Floating Point) questions

Consider the following floating-point format. Mantissa is a pure fraction in sign-magnitude form. The normalized representation for the above format is specified as follows. The mantissa has an implicit $1$ preceding the binary (radix) point. Assume that only $0’s$ are padded in while shifting a field. The normalized representation of the above number …

Consider the following floating-point format. Mantissa is a pure fraction in sign-magnitude form. The decimal number $0.239 \times 2^{13}$ has the following hexadecimal representation (without normalization and rounding off):

The hexadecimal representation of (657)8 is:

The range of integers that can be represented by an $n$ bit $2’s$ complement number system is:

Let $A = 1111 1010$ and $B = 0000 1010$ be two $8-bit$ $2’s$ complement numbers. Their product in $2’s$ complement is

What is the result of evaluating the following two expressions using three-digit floating point arithmetic with rounding? $(113. + -111.) + 7.51$ $113. + (-111. + 7.51)$

If $73_x$ (in base-x number system) is equal to $54_y$ (in base $y$-number system), the possible values of $x$ and $y$ are

The following is a scheme for floating point number representation using $16$ bits. Let $s, e,$ and $m$ be the numbers represented in binary in the sign, exponent, and mantissa fields respectively. Then the floating point number represented is: …

Assuming all numbers are in $2’s$ complement representation, which of the following numbers is divisible by $11111011$?

In $2's$ complement addition, overflow

Sign extension is a step in

The decimal value $0.25$

The $2's$ complement representation of the decimal value $-15$ is

The $2's$ complement representation of (-539)10 in hexadecimal is

Consider the values of $A = 2.0 \times 10^{30}, B = -2.0 \times 10^{30}, C = 1.0,$ and the sequence X:= A + B Y:= A + C X:= X + C Y:= Y + B executed on a computer where floating point numbers are represented with $32$ bits. The values for $X$ and $Y$ will be

The number $43$ in $2's$ complement representation is

Zero has two representations in

Booth's coding in $8$ bits for the decimal number $-57$ is:

Suppose the domain set of an attribute consists of signed four digit numbers. What is the percentage of reduction in storage space of this attribute if it is stored as an integer rather than in character form?

The octal representation of an integer is $(342)_8$. If this were to be treated as an eight-bit integer in an $8085$ based computer, its decimal equivalent is