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

2. Logic DesignLab 3. Full AdderChun-Hsien Ko Dept. of Electrical and Computer Eng., NCTU 2 Outlines Adder How to Design a Logic Circuit Half Adder and Full Adder DIP Switch Lab 3: 1-bit Full Adder

3. Logic DesignLab 3. Full AdderChun-Hsien Ko 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 3

4. Logic DesignLab 3. Full AdderChun-Hsien Ko 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 Dept. of Electrical and Computer Eng., NCTU 4 x y C S 0 0 0 1 1 0 0 1 1 1 1 0 x y S y x x y C

5. Logic DesignLab 3. Full AdderChun-Hsien Ko 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 Dept. of Electrical and Computer Eng., NCTU 5 C in

6. Logic DesignLab 3. Full AdderChun-Hsien Ko Design flow Draw truth table Then output is sum of product S = x y’C n ’ + x’y’C n + x yC n + x’yC n ’ = x  y  C n C n+1 = xy + xC n + yC n +xyC n = xy + xC n + yC n Dept. of Electrical and Computer Eng., NCTU 6

7. Logic DesignLab 3. Full AdderChun-Hsien Ko Using AND, OR, XOR to build a full adder 7408 (AND) 7486 (XOR) Dept. of Electrical and Computer Eng., NCTU 7 7432 (OR)

8. Logic DesignLab 3. Full AdderChun-Hsien Ko 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 8

9. Logic DesignLab 3. Full AdderChun-Hsien Ko 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” Dept. of Electrical and Computer Eng., NCTU 9 Connect to inputs

10. Logic DesignLab 3. Full AdderChun-Hsien Ko Resistor Network ( 排阻 ) Dept. of Electrical and Computer Eng., NCTU 10 Signal form here

11. Logic DesignLab 3. Full AdderChun-Hsien Ko 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 11