Question

QUESTION NO. 2:

a) Given ?(?, ?, ?, ?) = ? ′?? + ??? + ??? + ??′?′

I. Express F in the form of minterms

II. Find F’ and express it in the form of maxterms

III. Express the function F using minimum number of literals

IV. Draw the circuit for the function in step 3 using NOR gates only.

b) Given ? = ∏(1,3,4,6,9,10,11,12,14,15)

I. Express F in the form of maxterms

II. Find F’ and express in the form of minterms

III. Express the function F using minimum number of literals

IV. Draw the circuit for the function in step 3 using NAND gates only.

Answer 1

I)

(A+B+C'+D)(A+B+C'+D')(A+B'+C+D)(A+B'+C'+D)(A'+B+C+D')(A'+B+C'+D)(A'+B+C'+D')(A'+B'+C+D)(A'+B'+C'+D)(A'+B'+C'+D')

II)

Sigma(0, 2, 5, 7, 8, 13)

A'B'C'D' + A'B'CD' + A'BC'D + A'BCD + AB'C'D' + ABC'D

III)

Map 1 1 CD CD CD CD 0 0 0 0 0 0 0 0 0 0 1 А.В A.B A.B А.В 1 1 1 Map Layout 3 CD CD CD CD A.B 0 3 2 A.B 4 5 7 6 A.B 12 13 15 14 A.B 8 9 11 10 Groups (1,3,9,11) B.D (4,6,12,14) B.D (10,11,14,15)A.C

y=B.D+B.] +A.C = B.D+B.D+A.C y=(B+D') (B'+D) (A' + C')

F = (B + D') (B' + D) (A' + C')

IV)

B B D A с

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