A bank vault has three locks with a different key for each lock. Each key is own

Question

A bank vault has three locks with a different key for each lock. Each key is owned by a different person. To open the door, at least two people must insert their keys into the assignated lock. The signals A, B and C are 1 if there is a key inserted into lock 1, 2 or 3 respectively. The equation for the variable Z which is 1 iff the door should open is:

Question 22 options:

Z=AB + AC + BC

Z=ABC

Z=A + B + C

None of the above

A logic circuit realizing the function f has four inputs A, B, C and D. The three inputs A, B, C are the binary representation of the digits 0 through 7 with A being the most-significant bit. The input D is an odd-parity bit, ie the value of D is such that A, B, C and D allways contain an odd number of 1's. (For example, the digit 1 is represented by ABC = 001 and D = 0 and the digit 3 is represented by ABCD = 0111.) The function f has value 1 if the input digit is a prime number. (A number is prime if it divisible only by itself and 1; 2 is considered to be prime but 0 and 1 are not)

A list of the minterms and don't care minterms of f is :

f = ?m(4,7,11,14) + d(0,3,5,6,9,10,12,15)

f = ?m(2,3,5,7) + d(0,1,4,6,8,9,10,11,12,14,15)

f = ?m(2,3,5,7,11,13) + d(0,1,2,4,6,8,9,10,12,14,15)

None of the above

Z=AB + AC + BC

Z=ABC

Z=A + B + C

None of the above

Explanation / Answer

1)

if any two of A,B,C is true (i.e only two keys are sufficient...), then the function is 1

So F = AB + AC + BC

2)

Given function can be represented as this truth table

rest of the cases are dont care conditions

SO F = m4 + m7 + m11+ m14 + dont care conditions (m (0,3,5,6,9,10,12,15)

SO F = m(4,7,11,14) + d(0,3,5,6,9,10,12,15)

A B C D(odd parity) Prime or not (F) 0 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 1 1 1 1 1 0 0 0 0 1 0 1 1 1 1 1 0 1 0 1 1 1 0 1

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