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Digital Logic Structures: Chapter 3

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

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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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