ECE- 1551 DIGITAL LOGIC LECTURE 11: STANDARD CIRCUITS Assistant Prof. Fareena Saqib Florida Institute of Technology Fall 2015, 09/24/2015.

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Presentation transcript:

ECE DIGITAL LOGIC LECTURE 11: STANDARD CIRCUITS Assistant Prof. Fareena Saqib Florida Institute of Technology Fall 2015, 09/24/2015

Recap  Don’t Care Conditons  Karnaugh map of Product of Maxterms  Exclusive OR Function  Code Convertors  Excess 3

Agenda  Code Convertors  BCD to Gray Code  Parity Generator  BCD to 7 segment display decoder

Design Code Converters  Binary codes and how to develop code converters.  An n-bit binary code is a group of n bits that assumes up to 2^n distinct combinations of 1’s and 0’s. With each combination representing one element o the set that is being coded Combinational Logic IN OUT

Binary Codes  BCD, Binary representation of decimal numbers.  Excess 3  Gray Code  ASCII

Gray Code- Specification  Specification: Excess ‐ 3 is an unweighted code in which each coded combination is obtained from the corresponding binary value plus 3.  Application:its selfcomplementing property. Example 9’s complement of 3 is 6 and 6 9’s complement is 3.  Excess 3 representation of 3 is 0110 and of 6 is 1001  9’s complement of 3 only requires flipping the bits from 1 to 0 and 0 to 1 (as we did in 1’s complement).  Its not true in BCD where 3 is 0011 and 6 is We cannot directly calculate the 9’s complement.

Gray Code: Specification to truth table b3b2b1b0e3e2e1E

Gray Code:– Minimization using K-maps cd b1b0b1b g 0 = b 0 ’ b3b2b3b g 1 = (b 1 xor b 0 )’ g 2 = b 2 ’b 1 +b 2 b 1 ’b g 3 = b 3 +b 2 b 0 +b 2 b 1 b1b0b1b0 b3b2b3b2 b1b0b1b0 b3b2b3b2 b1b0b1b0 b3b2b3b2 g0g0 g1g1 g2g2 g3g3

Application 2: Parity Generator b3b2b1b0P

Parity Generator : K-maps cd b1b0b1b P 0 = ?? b3b2b3b2 P0P0

Parity Generator  Design circuit.  Discussed in class

BCD to 7 segment display decoder b3b2b1b0abcdefg

Parity Generator : K-maps XXXX 11XX cd b1b0b1b a= ?? b3b2b3b2 a XXXX XX cd b1b0b1b b= ?? b3b2b3b2 b XXXX XX cd b1b0b1b c= ?? c b3b2b3b2 XXXX XX cd b1b0b1b d= ?? d b3b2b3b2

Parity Generator : K-maps XXXX 11XX cd b1b0b1b e= ?? b3b2b3b2 e XXXX XX cd b1b0b1b f= ?? b3b2b3b2 f XXXX 11XX cd b1b0b1b g= ?? g b3b2b3b2