EE101-U3-BooleanAlgebra-Nazarian-Spring12

Help us manipulate logical expressionsequations

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Unformatted text preview: ) (A4’) (A5’) X = 1 if X ≠ 0 If X = 1, then X’ = 0 1+1=1 0+0=0 0+1=1+0=1 16 Single Variable Theorem (T1) X+0 = X (T1) XY 00 01 10 11 OR Z 0 1 1 1 Shahin Nazarian/EE101/Spring 2012 X•1 = X (T1’) X 0 0 1 1 Y 0 1 0 1 Z 0 0 0 1 AND 17 Single Variable Theorem (T2) X+1 = 1 (T2) X 0 0 1 1 Y 0 1 0 1 Z 0 1 1 1 OR Shahin Nazarian/EE101/Spring 2012 X•0 = 0 (T2’) XYZ 000 010 100 111 AND 18 Application Example: Channel Selector •  Given 4 input, digital music/sound channels and 4 output channels •  Given individual “select” inputs that select 1 input channel to be routed to 1 output channel 4 Input channels 011010101001101 ICH0 101010110101010 ICH1 001010101001011 ICH3 Input Channel Select Shahin Nazarian/EE101/Spring 2012 OSEL0 OSEL1 OSEL2 OSEL3 ICH2 ISEL0 ISEL1 ISEL2 ISEL3 101001010101111 Channel Selector OCH0 OCH1 OCH2 OCH3 4 Output channels Output Channel Select 19 Example: Steering Logic (Cont.) •  4-input music channels (ICHx) •  Select one input channel (use ISELx inputs) •  Route to one output channel (use OSELx inputs) 011010101001101 ICH0 0 0 0 ICH1 0 OCH 1 0 1 101001010101111 ICH2 0 OCH 2 0 0 001010101001011 ICH3 0 OCH 3 1 Shahin Nazarian/EE101/Spring 2012 OS EL2 OS EL1 O S EL0 IS EL3 IS EL2 IS EL1 IS EL0 0 OS EL3 101010110101010 OCH 0 20 Example: Steering Logic (Cont.) •  1st Level of AND gates act as barriers only passing 1 channel •  OR gates combines 3 streams of 0’s with the 1 channel that got passed (i.e. ICH1) •  2nd Level of AND gates passes the channel to only the selected output 0 Connection Point ICH1 0 0 ICH1 ICH1 ICH1 ICH1 1 ICH2 ICH1 0 0 ICH3 ICH1 0 Shahin Nazarian/EE101/Spring 2012 0 OCH 2 ICH1 OCH 3 1 OS EL2 0 00 1 OS EL1 OR: 0 + ICH1 + 0 + 0 = ICH1 O S EL0 IS EL3 IS EL2 IS EL1 IS EL0 0 10 0 0 OCH 1 0 0 AND: 1 AND ICHx = ICHx 0 AND ICHx = 0 0 OCH 0 0 OS EL3 ICH0 AND: 1 AND ICH1 = ICH1 0 AND ICH1 = 0 21 Single Variable Theorem (T3) X+X = X (T3) XY 00 01 10 11 OR Z 0 1 1 1 Shahin Nazarian/EE101/Spring 2012 X•X = X (T3’) X 0 0 1 1 Y 0 1 0 1 Z 0 0 0 1 AND 22 Single Variable Theorem (T4) (X) = X (T4) (X’)’ = X (T4) 0 Shahin Nazarian/EE101/Spring 2012 1 0 23 Single Variable Theorem (T5) X+X = 1 (T5) XY 00 01 10 11 OR Z 0 1 1 1 Shahin Nazarian/EE101/Spring 2012 X•X = 0 (T5’) XYZ 000 010 100 111 AND 24 Logic Functions English Schematic Shahin Nazarian/EE101/Spring 2012 25 Example •  B = H.D + K.D [Equation] •  Note: . has precedence over + H-) D - )--| >--H - )--| D-) [Schematic] •  Another version of eqn. and sch. •  [T.T.] T.T. is the only unique representation of a function Shahin Nazarian/EE101/Spring 2012 26 Example •  Converting T.T. to equation Shahin Nazarian/EE101/Spring 2012 27 Truth Tables Inputs I0 I1 I2 Circuit I2 I1 I0 All possible input combinations Shahin Nazarian/EE101/Spring 2012 O 0 O1 0 0 0 0 1...
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This note was uploaded on 03/13/2013 for the course EE 101 taught by Professor Redekopp during the Spring '06 term at USC.

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