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# De Morgan Theorem B[1]

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### Transcript

• 1. 1 Forging new generations of engineers
• 2. 2 DeMorgan’s Theorems
• 3. 3 DeMorgan’s Theorem #1 A · B = A + B EQUAL A B A x B A x B A B A + B 0 0 0 1 0 0 1 0 1 0 1 0 1 1 1 0 0 1 1 0 1 1 1 1 0 1 1 0
• 4. 4 DeMorgan’s Theorem #2 A B A + B A + B A B A x B 0 0 0 1 0 0 1 0 1 1 0 0 1 0 1 0 1 0 1 0 0 1 1 1 0 1 1 0 A + B = A · B EQUAL
• 5. 5 DeMorgan’s Theorem #1 A · B = A + B B A B A = Invert output of an AND gate Invert the inputs of an OR gate
• 6. 6 DeMorgan’s Theorem #2 A + B = A · B = Invert output of an OR gate Invert the inputs of an AND gate B A B A
• 7. 7 DeMorganizing an Expression XCBCACBCA =))(+(+)(+)( DeMorg. XCBCACBCA =)))(+(())(( DeMorg. XCBCACBCA =)))(+()(+)(( Dist. XCBCACACBCA =)))(+()(+( XCBCACBCA =)))(+()()((AA =
• 8. 8 DeMorganizing an Expression XCBCACACBCA =)))(+()(+( 0=AA XCBCAABCA =)))(+()(0+( 0=0A XCBCABCA =)))(+()(0+( DeMorg XCBCABCA =))(+)+)((( XCBCABCA =)))(+()((AA =0+
• 9. 9 DeMorganizing an Expression XCBCABCA =))(+)+)((( DeMorg XCBCABCA =))+(+))((( Assoc. XCBCABCA =)++)(( Dist. XCBCABBCACABCA =++ 0=0A XBABBCACBC =0++0 XBBCA =0++0AA =0+
• 10. 10 DeMorganizing an Expression XBBCA =0++0 AA =0+ XBBCA = XBCA =AAA =