1. Digital Logic Structures: Chapter 3 COMP 2610 Dr. James Money COMP 2610 1

2. Full Adder In order to implement a full adder circuit, let’s consider our method for adding binary numbers Recall that this is done in a similar way to long addition for decimal numbers

3. Full Adder Carry:100110000 110011010 +011011100 001110110

4. Full Adder Note that for each column of bits, we need three values: – Bit from value 1 - a i – Bit from value 2 - b i – Carry Bit – carry i

5. Full Adder The two outputs of the add are: – The result of the add is stored in s i – The carry value is stored in carry i+1 When can now formally turn this into a truth table for adding one bit

6. Full Adder aiai bibi carry i carry i+1 sisi 00000 00101 01001 01110 10001 10110 11010 11111

7. Full Adder

8. Figure 3.15 is on the previous slide

9. PLAs A Programmable Logic Array (PLA) is a common building block for building logical functions It consists of an array of AND gates, an array of OR gates, and some way to connect these outputs

10. PLAs

11. For a PLA, we consider a truth table with n inputs and m outputs You will need 2 n AND gates and m OR gates We then program the connections between the AND and OR gates The full adder is an example of this

12. Logical Completeness There is an important property to notice before we leave logic circuits called logical completeness We’ve shown that we only need AND, OR, NOT to form a logic circuit using PLAs We say {AND, OR, NOT} is logically complete because of this