GATE PYQ

Number System

Q11.
The 16 bit 2's complement representation of an integer is 1111 1111 1111 0101; its decimal representation is__________ .

Q12.
Let X be the number of distinct 16-bit integers in 2's complement representation. Let Y be the number of distinct 16 bit integers in sign magnitude representation. Then X-Y is ________.

Q13.
When two n-bit binary numbers are added the sum will contain at the most

Q14.
The binary equivalent of the decimal number 42.75 is

Q15.
Let the representation of a number in base 3 be 210. What is the hexadecimal representation of the number?

Q16.
How many different BCD numbers can be stored in 12 switches ? (Assume two position or on-off switches).

Q17.
The representation of the value of a 16-bit unsigned integer X in hexadecimal number system is BCA9. The representation of the value of X in octal number system is

Q18.
The number of 1's in the binary representation of (34096 + 15256 + 5*16 + 3) are:

Q19.
If (12A7C)_{16} = (X)_8 then the value of X is

Q20.
The number 1102 in base 3 is equivalent to 123 in which base system?