Digital-Grand Test -Q10

+1 vote

A logic circuit realizing the function f has four inputs a, b, c, d. The three inputs a, b, and 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; that is, the value of d is such that a, b, c, and d always contains 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(a,b,c,d) has value 1 if the input digit is a prime number. (A number is prime if it is divisible only by itself and 1; 1 is considered to be prime, and 0 is not.)

Which of the following is true for f ?

(A). F has 5 prime implicants and 5 essential prime implicants.

(B). F has 2 prime implicants and 2 essential prime implicants.

(C). F has 3 prime implicants and 2 essential prime implicants.

(D). F has 5 prime implicants and 0 essential prime implicants.

asked Jun 10 in Digital by gbeditor (44,560 points)
reshown Jun 12 by gbeditor

1 Answer

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Best answer

NOTE that the function has don't care values for the terms which cannot appear as input. 

 

The PI are : 

Cells (1,3,5,7,9,11,13,15) :  

Cells (2,3,10,11) : 

Cells(2,3,6,7)

Cells(0,1,2,3)

Cells(12,13)

NONE of these PI is an EPI because each 1 is being covered by more than one PI.

answered Jun 25 by deepak-gatebook (112,760 points)
Answer:
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