1. Dept. of Electrical and Computer Eng., NCTU
Lab 5. Full Adder
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
Adder
How to Design a Logic Circuit
Half Adder and Full Adder
DIP Switch
Lab 3: 1-bit Full Adder
Dept. of Electrical and Computer Eng., NCTU

3. Dept. of Electrical and Computer Eng., NCTU
Adder (Half Adder)
Describing binary summation of two one-bit binary inputs
Two inputs x and y
Two outputs C(carry) and S(sum)
Carry (C) is represented the carry out bit
Sum (S) is represented the sum of x and y
Black box can be represented as
Dept. of Electrical and Computer Eng., NCTU

4. Dept. of Electrical and Computer Eng., NCTU
Design flow
Draw truth table
We have 2 inputs (x and y), so there has 4 cases
List the corresponding output (C and S)
Then output is sum of product
S = x’y + x y’ = x  y
C = x y
x y C S x y S C
Dept. of Electrical and Computer Eng., NCTU

5. Dept. of Electrical and Computer Eng., NCTU
How to cascade the half adder?
Describing binary summation of three one-bit inputs
Three inputs and two outputs
Black box can be represented as
Cin
Dept. of Electrical and Computer Eng., NCTU

6. Dept. of Electrical and Computer Eng., NCTU
Design flow
Draw truth table
Then output is sum of product
S = x y’Cn’ + x’y’Cn + x yCn + x’yCn’ = x  y  Cn
Cn+1 = xy + xCn + yCn +xyCn = xy + xCn + yCn
Dept. of Electrical and Computer Eng., NCTU

7. Dept. of Electrical and Computer Eng., NCTU
Using AND, OR, XOR to build a full adder
7408 (AND)
7486 (XOR)
7432 (OR)
Dept. of Electrical and Computer Eng., NCTU

8. Dept. of Electrical and Computer Eng., NCTU
DIP switch (指撥開關)
Switch the High/Low voltage for Logic 1/0
Reserving the circuit of DIP switch for following experiments
The inner circuit of DIP switch
Dept. of Electrical and Computer Eng., NCTU

9. Dept. of Electrical and Computer Eng., NCTU
The related circuit of DIP switch
Use the 220Ω resistance (Red-Red-Brown)
When the switch of pin 16 and pin 1 is connected, the logic of input is “1”
When the switch of pin 16 and pin 1 is not connected, the logic of input is “0”
Connect to inputs
Dept. of Electrical and Computer Eng., NCTU

10. Dept. of Electrical and Computer Eng., NCTU
Resistor Network (排阻)
Signal form here
Dept. of Electrical and Computer Eng., NCTU

11. Dept. of Electrical and Computer Eng., NCTU
Lab 3: 1-bit Full Adder
Use DIP switch as the input signal
Use LED to display the outputs (carry and sum)
Question: How to extend to N-bit Adder?
Dept. of Electrical and Computer Eng., NCTU