1. Digital Logic Design Week 3
Logic gates
(NOT, AND, OR, NAND, NOR, XOR, XNOR)
Applications of Binary Codes (MOTIVATION)
(ASCII and UNICODE codes, Seven-segment Display Code, Gray code-rotation counter, Error Detection and Correction code)

2. Logic gates Logic gates Fixed-function logic & programmable logic
NOT gate
AND gate
OR gate
NAND gate
NOR gate
Exclusive-OR (XOR) and exclusive-NOR (XNOR) gates
Fixed-function logic & programmable logic

3. Basic logic operations and symbols
True only if all input conditions are true
AND OR
True only if one or more input conditions are true
NOT
Indicates the opposite condition X
True/false conditions are represented by voltages:
HIGH = true LOW = false

4. NOT gate also known as an inverter
performs inversion or complementation
HIGH ↔ LOW
1 ↔ 0

5. NOT gate Truth Table A X
A truth table shows the output corresponding to each possible input
Three equivalent ways to write the NOT condition:
X = NOT A
X = A’
We’ll use truth tables extensively in the course

6. NOT gate Timing diagram A X A X
Application: A group of inverters can be used to form the 1’s complement of a binary number:
Binary number
1’s complement

7. AND gate A B X
Produces a HIGH output when all inputs are HIGH; otherwise, the output is LOW

8. AND gate Truth table for a 2-input AND gateX
Truth table for a 2-input AND gate
0 0
0 1
1 0
1 1 1
AND operation is sometimes shown with a dot between the variables, but it may be implied (no dot):
AND operation is written as X = A·B or X = AB

9. AND gates have 2 or more inputs
#inputs = n
#input combinations (= #rows in truth table) = 2n
2 inputs → 22 = 4 input combinations
3 inputs → 23 = 8 input combinations
4 inputs → 24 = 16 input combinations
Write the truth table for a 3-input AND gate

10. AND gate A B X
Timing diagram

11. AND gate

12. OR gate A B X
Produces a HIGH output if any input is HIGH; if all inputs are LOW, the output is LOW

13. OR gate Truth table for a 2-input OR gateX
Truth table for a 2-input OR gate
0 0
0 1
1 0
1 1 1
The OR operation is shown with a plus sign (+) between the variables:
OR operation is written as X = A + B

14. OR gates have 2 or more inputs
Write the truth table for a 3-input OR gate

15. OR gate

16. NAND gate NAND = NOT-AND Truth table for a 2-input NAND gate
0 0
0 1
1 0
1 1 1
NAND operation is written as or

17. NOR gate NOR = NOT-OR Truth table for a 2-input NOR gate
0 0
0 1
1 0
1 1 1
NOR operation is written as or

18. Alarm to be activated if any door/window is open
Name the mystery gate #1
Alarm to be activated if any door/window is open ?

19. Name the mystery gate #2 ?

20. Name the mystery gate #3
Light turns on if this signal is LOW
????
Want green light ON if both tanks are at least 25% full
Level sensor output is HIGH if tank is at least 25% full

21. XOR gate
2-input exclusive-OR (XOR) gate produces a HIGH output if the inputs are at opposite logic levels
one HIGH & one LOW
Truth table for a 2-input XOR gate
0 0
0 1
1 0
1 1 1
XOR operation is written
3-input XOR defined:
extends to N-input XOR

22. XNOR gate A X B
2-input exclusive-NOR (XNOR) gate produces a HIGH output if the inputs are at same logic levels
both HIGH, or both LOW
Truth table for a 2-input XNOR gate
0 0
0 1
1 0
1 1 1
XNOR operation is written

23. Summary of logic gates

24. 1. The binary number 100011010100011011112 expressed in hexadecimal is:
(a) AD46716
(b) 8C46F16
(c) 8D46F16
(d) AE46F16
2. Convert the decimal number to hexadecimal

25. 3. Express the decimal number 246910 in binary-coded decimal.
4. A communication system transmits 9-bit blocks of information using an even parity scheme. The following byte of information is to be transmitted:
Calculate the value of the parity bit to be attached to this byte.

26. 5. For the set of input waveforms shown below, draw the timing diagram showing the output X in relation to the inputs.

27. 6. By examination of the timing diagram below, identify the type of 3-input gate which generates the output X. ?

28. 7. A 2-input gate with inputs A and B generates output X shown in the timing diagram below. The gate is:
an OR gate
an AND gate
a NOR gate
a NAND gate A X B

29. 9. The truth table for a 2-input NOR gate is:
0 0
0 1
1 0
1 1 1
0 0
0 1
1 0
1 1 1 a. b.
0 0
0 1
1 0
1 1 1
0 0
0 1
1 0
1 1 1 c. d.
© 2008 Pearson Education

30. 10. Compute the 2’s complement of 011011002
The decimal number is expressed in 8-bit 2’s complement form as:

31. 12. Write −3410 as a binary number in 8-bit 2’s complement form
13. Convert each of the following decimal numbers to 8-bit 2’s complement form, and add them: −52 and 25.
Check your answer by converting the result back to decimal.

32. 14. Convert the hexadecimal number 6B16 to octal (base-8)
15. Perform the following addition of hexadecimal numbers:
DF16 + AC16