Combinational Design, Part 2: Procedure

2 Topics Positive vs. negative logic Design procedure

3 Positive and Negative Logic Two different assignments of signal levels to logic values are possible 1.Using H level to represent a logic 1 (true) defines a positive logic system 2.Using H level to represent a logic 0 (true) defines a negative logic system

4 Assignment of Signal Levels to Logic Values

5 AND Gate Specification IC data sheets define gates in terms of both signal values and logic values Example: physical behavior specification of a CMOS gate What is the logic function implemented by this gate ??

6 Positive vs. Negative Logic a polarity indicator: signify that NEGATIVE LOGIC is assumed for the signal

7 Bottom Line Not much real change Negative logic functions are just duals of positive logic ones ♦ AND -> OR ♦ OR -> AND

8 Design Procedure Similar to software 1.Specification – problem description Write a specification for the circuit 2.Formulation – as truth table, Boolean function, or ( Verilog: in Lab) define the required relationships between inputs and outputs 3.Optimization – used to be manual, now CAD tool Draw a logic diagram or provide a netlist for the resulting circuit (AND, OR, INVERTORS) 4.Mapping – to select the implementation technology Transform the diagram or netlist to a new diagram or netlist using the available implementation technology 5.Verification – used to be manual, now simulation Verify correctness of design

9 Example 1 1.Specification: 3 binary inputs; Output is 1 when input < Formulation 3. Optimization 4. Mapping

10 5. Verification Verify correctness of design Manual: perform analysis of circuit Simulation

11 Analysis of Circuit Used in manual design verification and other purposes This shows a disciplined way to analyze a circuit ♦ To get Boolean function ♦ and/or Truth table

12 Derivation of Func. Or Table 1.Label gate outputs in terms of “input variables” ♦ Determine Boolean functions or values 2.Label outputs of gates fed by previously labeled gates ♦ Determine Boolean function or values 3.Repeat 2 until done

13 Let’s Do This Example

14 Derivation of Truth Table Make table with 2 n rows, where n is number of inputs Label some gate outputs Put those labels and the final outputs on columns of truth table Work your way across

15 Design Examples Design Examples in the book ♦ Study on your own: Example 3-1 (p.99) : Design of a BCD-to-Excess-3 Converter Example 3-2 (p.101) : Design of a BCD-Seven-Segment Decoder Examples 3-3 (Will do in class) : Design of a 4-bit Equality Comparator ♦ Input: 2 vectors A(3:0) and B(3:0) ♦ Output: One bit, E, which is 1 if A and B are bitwise equal, 0 otherwise

16 Design of a 4-bit Equality Comparator Specification : ♦ Input: 2 vectors A(3:0) and B(3:0) ♦ Output: One bit, E, which is 1 if A and B are bitwise equal, 0 otherwise Hierarchical design seems a good approach One module/bit Final module for E

17 Design for MX module Logic function E i =0 if A i and B i have the same value; E i = 1 if A i and B i have different values Can implement as

18 Design for ME module Final E is 1 only if all intermediate values are 0 So And a design is