1. CHAPTER 4 Analysis and Design of Combinational Logic (Sections 4.1 – 4.2)

2. Combinational Circuits A combinational circuit consists of logic gates whose outputs, at any time, are determined by combining the values of the inputs. A combinational circuit consists of logic gates whose outputs, at any time, are determined by combining the values of the inputs. For n input variables, there are 2 n possible binary input combinations. For n input variables, there are 2 n possible binary input combinations. For each binary combination of the input variables, there is one possible binary value on each output. For each binary combination of the input variables, there is one possible binary value on each output.

3. Combinational Circuits (cont.) Hence, a combinational circuit can be described by: Hence, a combinational circuit can be described by: Combinational Circuit.... x1x1 x2x2 xnxn ymym y2y2 y1y1 y3y3 Y 1 =f 1 (x 1,x 2,…,x n ) Y 2 =f 2 (x 1,x 2,…,x n ) Y m =f m (x 1,x 2,…,x n )...

4. Combinational vs. Sequential Circuits Combinational Circuit n-inputsm-outputs (Depend only on inputs) Combinational Circuit n-inputsm-outputs Storage Elements Next state Present state Sequential Circuit Combinational Circuit

5. Analysis of Combinational Logic Deriving Switching Equations Deriving Switching Equations Simplifying the switching equations Simplifying the switching equations Giving truth table Giving truth table Logic function conclussion Logic function conclussion

6. E.g. Analysis the functionality of the following circuit E.g. Analysis the functionality of the following circuit Analysis of Combinational Logic Y=(A’+B’)A+(A’+B’)B =A’B+AB’ Y=A ⊕ B

7. Analysis of Combinational Logic E.g. Analysis the functionality of the following circuit E.g. Analysis the functionality of the following circuit P 1 =(ABC)’ P 2 =A·P 1 =A·(ABC)’ P 3 =B·P 1 =B·(ABC)’ P 4 =C·P 1 =C·(ABC)’ F=(P2+P3+P4)’ =(A·(ABC)’+B·(ABC)’+C·(ABC)’)’ =((ABC)’(A+B+C))’ =ABC+A’B’C’  

8. Analysis of Combinational Logic  Giving truth table  Logic function conclussion

9. Combinational Circuit Design Design of a combinational circuit is the development of a circuit from a description of its function. Design of a combinational circuit is the development of a circuit from a description of its function. Starts with a problem specification and produces a logic diagram or set of boolean equations that represent the circuit. Starts with a problem specification and produces a logic diagram or set of boolean equations that represent the circuit.

10. Combinational Circuit Design 1. Determine the required number of inputs and outputs and assign variables to them. 2. Derive the truth table that defines the required relationship between inputs and outputs. 3. Obtain and simplify the Boolean function (K-maps, algebraic manipulation, CAD tools, … ). Consider any design constraints (area, delay, power, available libraries, etc). 4. Draw the logic diagram. 5. Verify the correctness of the design.

11. E.g1. Design a combinational circuit that will multiply two two-bit binary values E.g1. Design a combinational circuit that will multiply two two-bit binary valuesSolution: 1. input variables(A 1,A 0,B 1,B 0 ) output variables(P 3,P 2,P 1,P 0 ) output variables(P 3,P 2,P 1,P 0 ) Combinational Circuit Design

12. 2. Construct a truth table Combinational Circuit Design P 3 =f(A 1,A 0,B 1,B 0 )=∑(15) P 2 =f(A 1,A 0,B 1,B 0 )=∑(10,11,14) P 1 =f(A 1,A 0,B 1,B 0 )=∑(6,7,9,11,13,14) P 0 =f(A 1,A 0,B 1,B 0 )=∑(5,7,13,15) The output SOP equations are:

13. 3. The individually simplified equations are P 3 =A 1 A 0 B 1 B 0 P 2 =A 1 A 0 ’B 1 +A 1 B 1 B 0 ’ P 1 =A 1 ’A 0 B 1 +A 0 B 1 B 0 ’+A 1 B 1 ’B 0 +A 1 A 0 ’B 0 P 0 =A 0 B 0 Combinational Circuit Design

14. E.g.2 Design a combinational circuit that will accept a 2421BCD code and drive a TIL-312 seven-segment display E.g.2 Design a combinational circuit that will accept a 2421BCD code and drive a TIL-312 seven-segment display

15. Combinational Circuit Design

16. TRUTH TABLE

17. Combinational Circuit Design A=∑(1,10) B=∑(11,12) C=∑(8) D=∑(1,10,13) E=∑(1,9,10,11,13,15) F=∑(1,8,9,13) G=∑(0,1,13) A=w’z+x’yz’ B=xy’z’+x’yz C=wx’y’z’ D=xy’z+x’yz’+w’z E=x’y+z F=wx’y’+y’z G=w’+xy’z A=[(w’z)’(x’yz’)]’ B=[(xy’z’)’(x’yz)’] C=(wx’y’z’)’’ D=[(xy’z)’(x’yz’)’(w’z)’]’ E=[(x’y)’(z)’]’ F=[(wx’y’)’(y’z)’]’ G=[(w)(xy’z)’]’

18. Combinational Circuit Design

19. 4.2 Introduction to Digital IC IC package introduction IC package introduction IC category IC categoryTTLECLCMOS Low power(L) High speed(H) Low power Schottky(LS) Schottky(S) Advanced Low power Schottky(ALS) Advanced Schottky(AS)

20. IC naming regulation IC naming regulation 4.2 Introduction to Digital IC SN74LS00 manufacture 54--- military operating temperature range 74--- commercial temperature range Low power(L) High speed(H) Low power Schottky(LS) Schottky(S) Advanced Low power Schottky(ALS) Advanced Schottky(AS)

21. 4.2 Introduction to Digital IC

25. Exe.  