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

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

Full Adder Carry:

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

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

Full Adder aiai bibi carry i carry i+1 sisi

Full Adder

Figure 3.15 is on the previous slide

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

PLAs

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

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