GATE Digital Electronics

(A+B)(A+C) = ?

A + BC (distribution theorem)

AB + A’C + BC = ?

AB + A’C (concensus theorem)

(A+B)(A’+C) = ?

A’B + AC (transpose theorem)

(ABC)’ = ?

A’ + B’ + C’ (DeMorgan)

(A+B+C)’ = ?

A’.B’.C’ (DeMorgan)

No of terms that cannot be minimised for n variables?

2^(2^n)

How do you convert binary to gray code?

MSB = MSB, XOR of prev and current binary bit

What is gray code?

Each number differs from the next by a single bit

What is BCD?

each decimal digit has its own 4 bit sequence in which it is encoded

What is an implicant?

No of minterms

What is a false implicant?

No of maxterms

What is prime implicant?

Total no of required groups to form an expression

What is essential prime implicant?

Groups that are common in all ways of forming an expression

for an n-bit comparator, total no of combinations = ?

2^(2^n)

for an n-bit comparator, no of equal combinations = ?

2^n

for an n-bit comparator, no of unequal combinations = ?

2^(2^n) - 2^n

for an n-bit comparator, no of greater/lesser combinations = ?

(2^(2^n) - 2^n)/2

n bit parallel adder uses how many gates/blocks?

n-1 FA +1 HA or
2n-1 HA + n-1 OR
n FA

Maximum delay of n bit parallel adder when made using AND, XOR, OR

n-1 (Tand+Tor) + max{Tsum, Tcarry}

Maximum delay of n bit parallel adder when made using FA

n-1 (Tcarry) + max{Tsum, Tcarry}

What is a selective prime implicant?

Select one final expression out of all possible.
All prime implicants - essential = selective

What is a reduced prime implicant?

Select one final expression out of all possible.
All prime implicants - essential = selective
All prime implicants - essential of the other expressions = reduced

Range of n bit 1’s complement numbers?

-(2^n-1 - 1) to (2^n-1 - 1)

Maximum no of prime implicants = ?

2^n-1