GATE 2022: Digital Logic Quiz-1

What will be the value of x for the following expression?

(135)_x + (144)_x = (323)_x

Suppose the largest n-bit binary number requires 'd' digits in decimal representation. Which of the following relation is approximately correct?

Let A= 1100 1010 and B= 0000 0100 be two 8-bit 2's complement numbers. Their product in 2's complement is _______.

Consider the arithmetic expression -> (1100101)₂ -----(Gray code converter )---> ( X )_gray
Then what is the octal representation of the value X ?

Consider 2’s complement number system. Assume Decimal value of 11111011 is X. Then the value of X+10 in decimal is_____.

Consider a quadratic function x²-10x+21=0 having roots 3 and 7 in base b. So, the value of base b is _____.