1. 4–1

2. BSCS 5 th Semester

3. Introduction Logic diagram: a graphical representation of a circuit –Each type of gate is represented by a specific graphical symbol Truth table: defines the function of a gate by listing all possible input combinations that the gate could encounter, and the corresponding output

4. Gates There are six types of gates –NOT –AND –OR –XOR –NAND –NOR

5. NOT Gate A NOT gate accepts one input value and produces one output value

6. NOT Gate By definition, if the input value for a NOT gate is 0, the output value is 1, and if the input value is 1, the output is 0 A NOT gate is sometimes referred to as an inverter because it inverts the input value

7. AND Gate An AND gate accepts two input signals If the two input values for an AND gate are both 1, the output is 1; otherwise, the output is 0

8. OR Gate If the two input values are both 0, the output value is 0; otherwise, the output is 1

9. XOR Gate XOR, or exclusive OR, gate –An XOR gate produces 0 if its two inputs are the same, and a 1 otherwise –Note the difference between the XOR gate and the OR gate; they differ only in one input situation –When both input signals are 1, the OR gate produces a 1 and the XOR produces a 0

10. XOR Gate

11. NAND and NOR Gates The NAND and NOR gates are essentially the opposite of the AND and OR gates, respectively

12. Circuits Two general categories –combinational circuit –sequential circuit As with gates, we can describe the operations of entire circuits using three notations –Boolean expressions –logic diagrams –truth tables

13. Combinational Logic A combinational circuit consists of logic gates whose outputs at any Time are determined directly from the present combination of inputs without regard to previous inputs. –Output depends only on current input –Has no memory 4–13

14. Combinational Circuits Combinational Logic Circuit N input variables M output variables Block daigram of a combinational circuit

15. Combinational circuit: 1.Half Adder 2.Full Adder 4–15

16. Half Adders A circuit that computes the sum of two bits and produces the correct carry bit is called a half adder

17. Half Adder : Logic Diagram Circuit diagram representing a half adder Two Boolean expressions: sum = A  B carry = AB

18. Full Adders A circuit called a full adder takes the carry-in value into account

19. Sequential Logic Circuit It consist of a combinational circuit to which memory elements are connected to form a feedback path. The memory elements are devices capable of storing binary information with in them. -Output depends not only on current input but also on past input values, e.g., design a flip flop -Need some type of memory to remember the past input values

20. Flip Flops OR SR latch with NOR Gates The SR latch is a circuit with two cross-coupled NOR gates. It has two inputs labeled S for set and R for reset. Two states: Set (Q = 1) and Reset (Q = 0) When S=R=0, Q remains the same, S=R=1 is not allowed! Normally, S=R=0 unless the state need to be changed (memory?) State of the circuit depends not only on the current inputs, but also on the recent history of the inputs

21. Flip Flops with NAND Gates The SR latch is a circuit with two cross-coupled NAND gates. It has two inputs labeled S for set and R for reset. Two states: Set (Q = 0) and Reset (Q = 1) When S=R=1, Q remains the same S=R=0 is not allowed!

22. Examples of sequential systems Traffic light ATM Vending machine