1. Dept. of Electrical and Computer Eng., NCTU
Lab 2. NAND and XOR
Presenter: Chun-Hsien Ko
Contributors: Chung-Ting Jiang and Lin-Kai Chiu
Dept. of Electrical and Computer Eng., NCTU

2. Dept. of Electrical and Computer Eng., NCTU
Outlines
Learning how to put theory into practice
From equations to implementations
NAND and XOR
Boolean algebra representation of NAND
Truth table of NAND
Boolean algebra representation of XOR
Truth table of XOR
The logic transformation of different gates
LAB 2
Implement XOR by NAND gate
Dept. of Electrical and Computer Eng., NCTU

3. Dept. of Electrical and Computer Eng., NCTU
Boolean algebra representation of NAND
A NAND B = NOT(A AND B)
Y= (AB)’
Truth table of NAND
When S1 and S2 are ON, Q is equal to GND. Otherwise, Q is equal to VDD.
Input A
Input B
Output Y 1
Dept. of Electrical and Computer Eng., NCTU

4. Dept. of Electrical and Computer Eng., NCTU
Boolean algebra representation of XOR
XOR = exclusive OR
Y = A⊕B = AB’+A’B (sum of product)
Truth table of XOR
Input A
Input B
Output Y 1
Dept. of Electrical and Computer Eng., NCTU

5. Dept. of Electrical and Computer Eng., NCTU
LAB 2: Implement XOR by NAND gate
Experiment Materials
Bread board
Power supply
IC:7400 (4 NAND gates)
Light-emitting diode (LED)
Dept. of Electrical and Computer Eng., NCTU

6. Dept. of Electrical and Computer Eng., NCTU
Implement XOR by NAND gate
Y = A⊕B = AB’+A’B
Most of all digital circuits can be implemented by NAND gates
NOT gate: A’ = (AA)’
AND gate: AB = ((AB)’)’
OR gate: A+B = ((A’)(B’))’ with De Morgan's law
Combinational logic: AB+CD = ((AB)’(CD)’)’
Dept. of Electrical and Computer Eng., NCTU

7. Dept. of Electrical and Computer Eng., NCTU

8. Dept. of Electrical and Computer Eng., NCTU
A simple example
A XOR B = A AND B’ OR A’ AND B
= (A AND B’)’ NAND (A’ AND B)’
= (A’ NAND B) NAND (B’ NAND A)
= ((A NAND A) NAND B) NAND ( (B NAND B) NAND A)
Dept. of Electrical and Computer Eng., NCTU