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Digital Logic Structures: Chapter 3

This chapter delves into the implementation of full adder circuits, a fundamental component for binary addition. We explore the method for adding binary numbers using long addition principles, identifying key components such as the input bits and carry bits. The documentation also introduces Programmable Logic Arrays (PLAs) as crucial building blocks for creating logical functions, detailing their structure with AND and OR gates, and emphasizing the concept of logical completeness, which states that we only require AND, OR, and NOT gates to construct a complete logic circuit.

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Digital Logic Structures: Chapter 3

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

  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 - ai • Bit from value 2 - bi • Carry Bit – carryi

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

  6. Full Adder

  7. Full Adder

  8. Full Adder 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. PLAs • For a PLA, we consider a truth table with n inputs and m outputs • You will need 2n 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

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