Download to read offline
Pycology Chap 5.pptxPycology Chap 5.pptxPycology Chap 5.pptxPycology Chap 5.pptx
- 1.
- 2. East Africa University ComputerScience & IT
- 3. http://www.mahergelle.com By Eng.Adulahi M.Adan Digital Logic Design
- 4.
- 5. Digital Circuits Digital circuitsare classified into two types 1. combinational circuits 2. sequential circuits Digital Logic Design
- 6. Combinational Circuits 1. Introductionto Combinational Circuits • Definition A Combinational Circuit is a digital logic circuit in which: The output depends only on the present input There is NO memory There is NO feedback The output changes immediately when input changes • General Formula Digital Logic Design
- 7. Combinational Circuits • Theoutput of a combinational circuit depends on its present inputs only. • The block diagram of a combinational circuit with m inputs and n outputs is shown in below figure Digital Logic Design
- 8. Combinational Circuits Real-Life Examples Calculator Voting machine Digital thermometer Traffic light controller (simple version) ALU inside the CPU Digital Logic Design
- 9. Combinational circuit DesignProcedure: • It involves following steps : • Step 1 : From the word description of the problem, identify the inputs and outputs and draw a block diagram. • Step 2 : Make a truth table based on problem • Step 3 : Simplified output functions are obtained by algebraic manipulation, k-map method or tabular method. • Step 4 : Implement the simplified expression using logic gates. Digital Logic Design
- 10. Example: • A TVis connected through three switches. The TV becomes ‘on’ when at least two switches are in ‘ON’ position; • In all other conditions, TV is ‘OFF’. SOL • Step I :- The TV is connected with 3 switches; thus there are three inputs to TV, represented by variables say A, B and C. The o/p of TV is represented by variable say, F. Digital Logic Design
- 11. Example: • Step 2:-0 → switch off 1 → switch on Digital Logic Design TV SWITCHES INPUTS OUTPUT A B C F 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 1 1 0 0 0 1 0 1 1 1 1 0 1 1 1 1 1
- 12. Example: Step 3:- Usinga 3 variable K-map, we can simplify the function obtained in step 2 F = AB+AC+BC Digital Logic Design
- 13. Example: Step 4:- Forimplementation we need three ‘AND’ gates and one ‘OR’ gate as shown in Fig. Digital Logic Design
- 14. Combinational Circuits (usesLogic Gates) • a Digital Logic Design
- 15. Combinational Circuits (usesLogic Gates) • a Digital Logic Design
- 16. HALF ADDER Step1:- Ithas two inputs A and B. that are two 1-bit members, and two output sum (S) and carry (C) produced by addition of two bits Figure: Half adder Digital Logic Design
- 17. HALF ADDER Step 2:-Truth Table for Half Adder Digital Logic Design
- 18. HALF ADDER Step 3:-Using a two variable k-map, separately for both outputs S and C. Digital Logic Design
- 19. HALF ADDER Step 4:-Logical Implementation (i) Using Basic gates Digital Logic Design
- 20. HALF ADDER (ii) UsingXOR gate Digital Logic Design
- 21. Half-Adder The most basicdigital arithmetic circuit. Performs the addition of two binary digits. The input variables of a half-adder are called the augends and the addend. The output variables of a half-adder are called the sum and the carry. Fig: half adder S = x’y+xy’=x y ⊕ C=xy 21
- 22. FULL ADDER Full adderis a combinational circuit that performs the addition of three binary digits Step 1:- It has three inputs A, B and C and two outputs S and C0 produced by addition of three input bits. Digital Logic Design
- 23. FULL ADDER Step 2:-Truth Table for the full adder Digital Logic Design
- 24. FULL ADDER Step 3:-Using a three variable map for both outputs. Digital Logic Design
- 25. FULL ADDER Step 4:-Logical Implementation (i) Using Basic Gates Digital Logic Design
- 26. FULL ADDER Applications offull adder circuit:- • ALU in computers and varieties of calculators • Different IC and microprocessor chips in PC n laptops • Ripple counter • Important tool in DSP(digital signal processing) Digital Logic Design
- 27. HALF SUBTRACTOR Step 1:-The half subtractor is a combinational circuit which is used to perform the subtraction of two bits. Digital Logic Design
- 28. HALF SUBTRACTOR Step 3:-Using a two variable map, for outputs D and B. Digital Logic Design
- 29. HALF SUBTRACTOR Step 4:-Logical Implementation shown in Figures (a) Using Basic gate Digital Logic Design
- 30. HALF SUBTRACTOR (b) usingXOR gate Digital Logic Design
- 31. FULL SUBTRACTOR Step 1:-Full subtractor is a combinational circuit that performs the subtraction of three binary digits. Digital Logic Design INPUTS OUTPUTS A B C DIFFERENCE D BORROW B0 0 0 0 0 0 0 0 1 1 1 0 1 0 1 1 0 1 1 0 1 1 0 0 1 0 1 0 1 0 0 1 1 0 0 0 1 1 1 1 1
- 32. FULL SUBTRACTOR Step 3:-Using a three variable map for both outputs. Digital Logic Design
- 33. FULL SUBTRACTOR Step 4:-Logical implementation (i) Using logic symbols DO EXERCISE AND DRAW THE CIRCUIT Digital Logic Design
- 34. Reading Topics • Multiplexer(reading) •Demultiplexer (Reading) • Encoder • Decoder Digital Logic Design
- 35.
- 36.