1. Digital Fundamentals Floyd Chapter 3 Tenth Edition
© 2008 Pearson Education

2. Outline 3-1 The Inverter 3-2 The AND Gate 3-3 The OR Gate
3-4 The NAND Gate
3-5 The NOR Gate
3-6 The Exclusive-OR and Exclusive-NOR Gates
3-7 Fixed Function Logic
3-8 Programmable Logic

3. The Inverter A X
The inverter performs the Boolean NOT operation. When the input is LOW, the output is HIGH; when the input is HIGH, the output is LOW.
LOW (0) HIGH (1)
HIGH (1) LOW(0)
The NOT operation (complement) is shown with an overbar. Thus, the Boolean expression for an inverter is 𝑋= 𝐴 .

4. The Inverter Example waveforms: A X
A group of inverters can be used to form the 1’s complement of a binary number:
Binary number
1’s complement

5. Outline 3-1 The Inverter 3-2 The AND Gate 3-3 The OR Gate
3-4 The NAND Gate
3-5 The NOR Gate
3-6 The Exclusive-OR and Exclusive-NOR Gates
3-7 Fixed Function Logic
3-8 Programmable Logic

6. The AND Gate A X B
The AND gate produces a HIGH output when all inputs are HIGH; otherwise, the output is LOW. For a 2-input gate, the truth table is
0 0
0 1
1 0
1 1 1
The AND operation is usually shown with a dot between the variables but it may be implied (no dot). Thus, the AND operation is written as X = A .B or X = AB.

7. The AND Gate Example Example waveforms: A B X
The AND operation is used in computer programming as a selective mask. If you want to retain certain bits of a binary number but reset the other bits to 0, you could set a mask with 1’s in the position of the retained bits.
If the binary number is ANDed with the mask , what is the result?
Example

8. The AND Gate
Example
In an automobile seat belt alarm system, when will the alarm go off?

9. Outline 3-1 The Inverter 3-2 The AND Gate 3-3 The OR Gate
3-4 The NAND Gate
3-5 The NOR Gate
3-6 The Exclusive-OR and Exclusive-NOR Gates
3-7 Fixed Function Logic
3-8 Programmable Logic

10. The OR Gate A X B
The OR gate produces a HIGH output if any input is HIGH; if all inputs are LOW, the output is LOW. For a 2-input gate, the truth table is
0 0
0 1
1 0
1 1 1
The OR operation is shown with a plus sign (+) between the variables. Thus, the OR operation is written as X = A + B.

11. The OR Gate Example Example waveforms: A B X
The OR operation can be used in computer programming to set certain bits of a binary number to 1.
ASCII letters have a 1 in the bit 5 position for lower case letters and a 0 in this position for capitals. (Bit positions are numbered from right to left starting with 0.) What will be the result if you OR an ASCII letter with the 8-bit mask ?
Example

12. ASCII
Solution
The resulting letter will be lower case.

13. The OR Gate
Example
When will the alarm go off in an intrusion detection system?

14. Outline 3-1 The Inverter 3-2 The AND Gate 3-3 The OR Gate
3-4 The NAND Gate
3-5 The NOR Gate
3-6 The Exclusive-OR and Exclusive-NOR Gates
3-7 Fixed Function Logic
3-8 Programmable Logic

15. The NAND Gate A X B
The NAND gate produces a LOW output when all inputs are HIGH; otherwise, the output is HIGH. For a 2-input gate, the truth table is
0 0
0 1
1 0
1 1 1
The NAND operation is shown with a dot between the variables and an overbar covering them. Thus, the NAND operation is written as 𝑋= 𝐴∙𝐵 (Alternatively, 𝑋= 𝐴𝐵 .)

16. The NAND Gate Question A B X Example waveforms:
How would you connect a 2-input NAND gate to form a basic inverter?
Question

17. The NAND Gate Example NAND gate acts as negative-OR gate 0 0 0 1 1 0
Input
Intermediate
Output
A B X
0 0
0 1
1 0
1 1 1
0 0
0 1
1 0
1 1
1 1
1 0
0 1
0 0 1

18. The NAND Gate
Example
NAND gate acts as negative-OR gate

19. Outline 3-1 The Inverter 3-2 The AND Gate 3-3 The OR Gate
3-4 The NAND Gate
3-5 The NOR Gate
3-6 The Exclusive-OR and Exclusive-NOR Gates
3-7 Fixed Function Logic
3-8 Programmable Logic

20. The NOR Gate A X B
The NOR gate produces a LOW output if any input is HIGH; if all inputs are HIGH, the output is LOW. For a 2-input gate, the truth table is
0 0
0 1
1 0
1 1 1
The NOR operation is shown with a plus sign (+) between the variables and an overbar covering them. Thus, the NOR operation is written as 𝑋= 𝐴+𝐵 .

21. The NOR Gate Example Solution A B X Example waveforms:
The NOR operation will produce a LOW if any input is HIGH.
Example
When is the LED is ON for the circuit shown?
Solution
The LED will be on when any of the four inputs are HIGH.

22. The NOR Gate Example NOR gate acts as negative-AND gate 0 0 0 1 1 0
Input
Intermediate
Output
A B X
0 0
0 1
1 0
1 1 1
0 0
0 1
1 0
1 1
1 1
1 0
0 1
0 0 1

23. The NOR Gate
Example
Aircraft landing monitoring system

24. Outline 3-1 The Inverter 3-2 The AND Gate 3-3 The OR Gate
3-4 The NAND Gate
3-5 The NOR Gate
3-6 The Exclusive-OR and Exclusive-NOR Gates
3-7 Fixed Function Logic
3-8 Programmable Logic

25. The XOR Gate A X B
The XOR gate produces a HIGH output only when both inputs are at opposite logic levels. The truth table is
0 0
0 1
1 0
1 1 1
The XOR operation is written as 𝑋= 𝐴 𝐵+𝐴 𝐵 . Alternatively, it can be written with a circled plus sign between the variables as 𝑋=𝐴⨁𝐵.

26. The XOR Gate Question A B X Example waveforms:
Notice that the XOR gate will produce a HIGH only when exactly one input is HIGH.
If the A and B waveforms are both inverted for the above waveforms, how is the output affected?
Question
There is no change in the output.

27. The XOR Gate
Example
XOR Gate used as a two-bit modulo-2 adder

28. The XNOR Gate A X B
The XNOR gate produces a HIGH output only when both inputs are at the same logic level. The truth table is
0 0
0 1
1 0
1 1 1
The XNOR operation shown as 𝑋= 𝐴𝐵 + 𝐴𝐵. Alternatively, the XNOR operation can be shown with a circled dot between the variables. Thus, it can be shown as X = A . B.

29. The XNOR Gate A X B
The XNOR gate produces a HIGH output only when both inputs are at the same logic level. The truth table is
0 0
0 1
1 0
1 1 1
The XNOR operation shown as 𝑋= 𝐴 𝐵 +𝐴𝐵. Alternatively, the XNOR operation can be shown with a circled dot between the variables. Thus, it can be shown as 𝑋=𝐴⊙𝐵.

30. The XNOR Gate Question A B X Example waveforms:
Notice that the XNOR gate will produce a HIGH when both inputs are the same. This makes it useful for comparison functions.
If the A waveform is inverted but B remains the same, how is the output affected?
Question
The output will be inverted.

31. Outline 3-1 The Inverter 3-2 The AND Gate 3-3 The OR Gate
3-4 The NAND Gate
3-5 The NOR Gate
3-6 The Exclusive-OR and Exclusive-NOR Gates
3-7 Fixed Function Logic
3-8 Programmable Logic

32. Fixed Function Logic Cannot be programmed Two Major families:
TTL: transistor-transistor logic
CMOS: complementary metal-oxide semi-conductor (more prevalent)
Examples:
DIP package SOIC package

33. 74 series NAND gate device
Fixed Function Logic
Logic symbols show the gates and associated pin numbers.
74xx00
74 series NAND gate device
74xx27
74 series NOR gate device

34. Fixed Function Logic
Some common gate configurations are shown.

35. Fixed Function Logic
Data sheets include limits and conditions set by the manufacturer as well as DC and AC characteristics. For example, some maximum ratings for a 74HC00A are:

36. Outline 3-1 The Inverter 3-2 The AND Gate 3-3 The OR Gate
3-4 The NAND Gate
3-5 The NOR Gate
3-6 The Exclusive-OR and Exclusive-NOR Gates
3-7 Fixed Function Logic
3-8 Programmable Logic

37. Programmable Logic
A Programmable Logic Device (PLD) can be programmed to implement logic. There are various technologies available for PLDs. Many use an internal array of AND gates to form logic terms. Many PLDs can be programmed multiple times.

38. Programmable Logic
A Programmable Logic Device (PLD) can be programmed to implement logic. There are various technologies available for PLDs. Many use an internal array of AND gates to form logic terms. Many PLDs can be programmed multiple times.

39. Programmable Logic
In general, the required logic for a PLD is developed with the aid of a computer. The logic can be entered using a Hardware Description Language (HDL) such as VHDL. Logic can be specified to the HDL as a text file, a schematic diagram, or a state diagram.

40. Programmable Logic entity NandGate is port(A, B: in bit;
LED: out bit);
end entity NandGate;
architecture GateBehavior of NandGate is
signal A, B: bit;
begin
X <= A nand B;
LED <= X;
end architecture GateBehavior;

41. Selected Key Terms Inverter Truth table Timing diagram Boolean algebra
AND gate
A logic circuit that inverts or complements its inputs.
A table showing the inputs and corresponding output(s) of a logic circuit.
A diagram of waveforms showing the proper time relationship of all of the waveforms.
The mathematics of logic circuits.
A logic gate that produces a HIGH output only when all of its inputs are HIGH.

42. Selected Key Terms OR gate NAND gate NOR gate Exclusive-OR gate
Exclusive-NOR gate
A logic gate that produces a HIGH output when one or more inputs are HIGH.
A logic gate that produces a LOW output only when all of its inputs are HIGH.
A logic gate that produces a LOW output when one or more inputs are HIGH.
A logic gate that produces a HIGH output only when its two inputs are at opposite levels.
A logic gate that produces a LOW output only when its two inputs are at opposite levels.