NANDNOR Implementation q NAND comes only with AND

NAND/NOR Implementation q NAND comes only with AND q NOR comes only with OR NOR = OR NAND = AND q To convert an expression to NAND, all ORs should be converted to ANDs “Complement Twice” q To convert an expression to NOR, all ANDs should be converted to ORs “Complement Twice” q In the end, make sure that each logical operator have a BAR for complement. Otherwise, make an extra complement twice. CPIT 210 LAB, 2009 Amal Alkhaldi

NA ND Example: simplify the following function using only NAND A. B + C. D AND/OR expression We want to convert it to NAND expression CPIT 210 LAB, 2009 Amal Alkhaldi

NA ND 1 Complement each OR twice ( A. B + C. D )’’ Complement the only OR twice for expression unchanged CPIT 210 LAB, 2009 Amal Alkhaldi

NA ND 1 Complement each OR twice ( (A. B)’. (C. D)’ )’ First Complement CPIT 210 LAB, 2009 Second Complement Amal Alkhaldi

NA ND 2 Make sure each operator had a BAR ( (A. B)’. (C. D)’ )’ Finished… Each operator had a BAR CPIT 210 LAB, 2009 Amal Alkhaldi

NO R Example: simplify the following function using only NOR A. B + C. D AND/OR expression We want to convert it to NOR expression CPIT 210 LAB, 2009 Amal Alkhaldi

NO R 1 Complement each AND twice (A. B)’’+ (C. D)’’ Complement each AND twice for expression unchanged CPIT 210 LAB, 2009 Amal Alkhaldi

NO R 1 Complement each AND twice (A’+B’)’+ (C’+D’)’ First Complement CPIT 210 LAB, 2009 Second Complement First Complement Second Complement Amal Alkhaldi

NO R 2 Make sure each operator had a BAR (A’+B’)’+ (C’+D’)’ This operator with a BAR CPIT 210 LAB, 2009 This operator still without a BAR Remember It should has a BAR because NOR = OR This operator with a BAR Amal Alkhaldi

NO R 2 Make sure each operator had a BAR ((A’+B’)’+ (C’+D’)’)’’ NOW it has a BAR Remember We complement twice for expression unchanged CPIT 210 LAB, 2009 Amal Alkhaldi

LAB Example 1: simplify the following function using only (I)NAND (II)NOR X Y’ + Y Z + X’ Y’ Z’ NAND X Y’ + Y Z + X’ Y’ Z’ (X Y’ + Y Z + X’ Y’ Z’)’’ ( (X Y’)’. (Y Z)’. (X’ Y’ Z’)’ )’ Original Expression with one OR complement the expression twice to get the AND Finish , each operator had a BAR NOR X Y’ + Y Z + X’ Y’ Z’ (X Y’ )’’+ (Y Z)’’+ (X’ Y’ Z’)’’ (X’+Y )’+ (Y’+Z’)’+ (X+Y+Z)’ ( (X’+Y )’+ (Y’+Z’)’+ (X+Y+Z)’ )’’ Original Expression with one 3 AND complement each AND expression twice to get the OR 3 OR operators with complement, one OR without a BAR make an extra complement Finish , each operator had a BAR (we made a twice complement to unchanged expression) CPIT 210 LAB, 2009 Amal Alkhaldi

LAB Example 2: simplify the following function using only (I)NAND (II)NOR X’ Y + (X+Z’) (Y+Z) NAND X’ Y + (X + Z’) (Y + Z) (X’ Y + (X + Z’)’’ (Y + Z)’’ (X’ Y + (X’ Z)’ (Y’ Z’)’ )’’ ((X’ Y)’ ( (X’ Z)’ (Y’ Z’)’)’ )’ NOR X’ Y + (X + Z’) (Y + Z) (X’ Y)’’ + ((X + Z’) (Y + Z))’’ (X+Y’)’ + ((X + Z’)’+(Y + Z)’)’ ((X+Y’)’ + ((X + Z’)’+(Y + Z)’)’ )’’ Original Expression with one 3 OR complement each OR expression twice to get the AND Complement the inner 2 ORs Complement the third OR Finish , each operator had a BAR Original Expression with one 2 AND complement each AND expression twice to get the OR 4 ORs operators with complement, one OR without a BAR make an extra complement Finish , each operator had a BAR (we made a twice complement to unchanged expression) CPIT 210 LAB, 2009 Amal Alkhaldi