Essentials of Combinational Circuits. PPTX
- 1. DIGITAL LOGIC CIRCUITS By N.SRI PRAKASH,B.Tech,M.Tech(Ph.D)
- 2. • Digital circuits are classified into two types 1. combinational circuits 2. sequential circuits
- 3. COMBINATIONAL CIRCUITS • The output 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
- 4. Combinational circuit Design Procedure: 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 statement which completely describes the operations of circuit for different combinations of inputs. 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.
- 5. Example: A TV is connected through three switches. The TV becomes ‘on’ when atleast two switches are in ‘ON’ position; In all other conditions, TV is ‘OFF’.
- 6. 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.
- 7. Step 2:- 0 → switch off 1 → switch on 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
- 8. • Step 3:- In general, in simplifying boolean functions upto four variables, the best method is K-map technique. Thus, using a 3 variable K-map, we can simplify the function obtained in step 2 F = AB+AC+BC
- 9. • Step 4:- For implementation we need three ‘AND’ gates and one ‘OR’ gate as shown in Fig.
- 10. ARITHMATIC CIRCUITS • The logic circuits which are used for performing the digital arithmatic operations such as addition, subtraction, multiplication and division are called ‘arithmatic circuits’.
- 11. HALF ADDER Step1:- It has 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
- 12. • Step 2:- Truth Table for Half Adder
- 13. • Step 3:- Using a two variable k-map, separately for both outputs S and C.
- 14. • Step 4:- Logical Implementation (i) Using Basic gates
- 15. (ii) Using XOR gate
- 16. FULL ADDER • Full adder is 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.
- 17. Step 2:- Truth Table for the full adder
- 18. Step 3:- Using a three variable map for both outputs.
- 19. • Step 4:- Logical Implementation (i) Using Basic Gates
- 20. • A full adder can also be implemented using two half adders The sum part is
- 21. • The carry part is
- 22. • Therefore
- 24. Applications of full 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)
- 25. HALF SUBTRACTOR Step 1:- The half subtractor is a combinational circuit which is used to perform the subtraction of two bits.
- 26. Step 2:- Truth Table • The difference output is 0 if A = B and 1 if A ≠ B; the borrow output is 1 whenever A < B. If A < B, the subtraction is done by borrowing 1 from the next higher order bit.
- 27. Step 3:- Using a two variable map, for outputs D and B.
- 28. Step 4:- Logical Implementation shown in Figures (a) Using Basic gates
- 29. (b) using XOR gate
- 30. FULL SUBTRACTOR Step 1:- Full subtractor is a combinational circuit that performs the subtraction of three binary digits.
- 31. Step 2:- Truth Table 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. Step 3:- Using a three variable map for both outputs.
- 33. Step 4:- Logical implementation (i) Using logic symbols DO EXERCISE AND DRAW THE CIRCUIT
- 34. • A ‘full subtractor’ can also be implemented using two ‘half subtractors’ and an ‘OR’ gate as shwon in Fig. • The Difference
- 35. • The Borrow is
- 37. • Block Diagram Representation of a full subtractor using two half subtractors
- 39. 4 BIT BINARY SUBTRACTOR
- 41. Alternate diagram for adder-subtractor
- 42. • In the above figure the addition and subtraction operations are combined into one circuit with one common binary adder. • This is done by including an XOR gate with each full-adder. • The mode input M controls the operation. When M=0, the circuit is an adder. When M=1, the circuit becomes a subtractor. • Each XOR gate receives input M and one of the inputs of B. • When M=0, we have B0=B. • The full-adder receives the value of B, the input carry is 0 and the circuit performs A+B. • When M=1, we have B1= B’ and C1=1. the B inputs are complemented and a 1 is added through the input carry. • The circuit performs the operation A plus the 2’s complement of B.
Editor's Notes
- #15: Half adder using xor logic gate