1. Combinational Logic Design

2. Combinatorial Logic Circuit m Boolean Inputs n Boolean Outputs Combinational Circuits • A combinational logic circuit has: • A set of m Boolean inputs, • A set of n Boolean outputs • n switching functions, each mapping the 2m input combinations to an output such that the current output depends only on the current input values A block diagram

3. Design Procedure • Specification • Write a specification for the circuit if one is not already available • Formulation • Derive a truth table or initial Boolean equations that define the required relationships between the inputs and outputs, if not in the specification • Apply hierarchical design if appropriate (more later)

4. Design Procedure 3. Optimization • Apply 2-level and multiple-level optimization • Draw a logic diagram for the resulting circuit using ANDs, ORs, and inverters

5. Design Procedure • Technology Mapping • Map the logic diagram or netlist to the implementation technology selected • Verification • Verify the correctness of the final design manually or using simulation

6. Hierarchical Design • Objective: To control the complexity of each function which is mapping inputs to outputs • Decompose the function into smaller pieces called blocks • Decompose each block’s function into smaller blocks, repeating as necessary until all blocks are small enough • Any block not decomposed is called a primitive block • The collection of all blocks including the decomposed ones is a hierarchy

7. Example: 9-input even parity checker • Design a 9-input function to check even parity for byte • Chapter 2: Use odd function circuit to check even parity

8. We know how to design a 3-input odd function

9. We know how to design an XOR Y X • A NAND only implementation is: X Y

10. Design Hierarchy

11. The blocks that must be designed Components in Design

12. 9-input parity tree (continued) • Top Level: 9 inputs, one output • 2nd Level: Four 3-bit odd funcions in two levels • 3rd Level: Two 2-bit exclusive-OR functions • Primitive block, XOR gate: Four 2-input NAND gates • Design requires {4 X (2 X 4)} = 32 2-input NAND gates

13. Top Down Design • Ideally you specify top level of design and work your way down • Real life isn’t that way • Work some at top • Build/test some low-level blocks • Go back to top level • Just like real software programs • Big projects (like Pentium) done with architecture and levels of simulators