NAND, Two-Level Implementations, Parity

Tom Kelliher, CS 240

Feb. 10, 2006

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Collect homework assignments.

Assignment

Read 2.8.

New homework assignment.

From Last Time

Simplifying K-maps.

Outline

1. NAND gates.

2. Two-level physical realizations.

3. Parity generation and checking.

4. BCD to 7-segment decoder example.

Coming Up

Circuit technologies.

NAND Gates

1. Not AND. Symbol. Truth table.

2. At the physical level, this is what we work with.

3. Completeness: Given a two-input NAND show how to implement inverter, AND, OR.

4. NOR completely analogous.

Physical Realizations

Given that we only have NAND gates, implement: $ABC + DEF + GHI$. (Draw using AND and OR, derive NAND implementation, and draw.)

Parity Generation and Checking

1. EXOR symbol, truth table.

2. EXOR = odd function. (NEXOR = even)

3. A ``big'' EXOR can be recursively constructed from ``small'' EXORs.

4. Parity generate and check circuit for ASCII data:

   
   

   figure=Figures/parity.eps

   
   

   Show a few examples.

Example: BCD to 7-Segment Decoder

Simplify and implement $\rm S_4$.

Tom Kelliher