Number System in Digital logic PYQ quiz GATE CS

The smallest integer that can be represented by an 8-bit number in 2’s complement form is

P is a 16-bit signed integer. The 2's complement representation of P is (F87B)₁₆.The 2's complement representation of 8*P
 

What is the minimum number of gates required to implement the Boolean function (AB+C) if we have to use only 2-input NOR gates?

(1217)₈ is equivalent to

The hexadecimal representation of 657₈ 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?

If x and y are two decimal digits and (0.1101)₂ = (0.8xy5)₁₀, the decimal value of x+y is _____ .

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

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 _________ [This Question was originally a Fill-in-the-blanks Question]

We want to design a synchronous counter that counts the sequence 0-1-0-2-0-3 and then repeats. The minimum number of J-K flip-flops required to implement this counter is   Note : This question was asked as Numerical Answer Type.