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GATE 2022: Digital Logic Quiz-1

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Question 1

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

(135)x + (144)x = (323)x

Question 2

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

Question 3

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

Question 4

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

Question 5

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

Question 6

Consider a quadratic function x2-10x+21=0 having roots 3 and 7 in base b. So, the value of base b is _____.
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May 23GATE & PSU CS