1 / 21

The Digital Logic Level

The Digital Logic Level. Computer Organization Lecture #6 Jahan Zeb. Gates and Boolean Algebra.

atalo
Télécharger la présentation

The Digital Logic Level

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. The Digital Logic Level Computer Organization Lecture #6 Jahan Zeb

  2. Gates and Boolean Algebra • The symbols and functional behavior for the five basic gates. • Boolean function of n variable is completely described by table with 2n rows, known as truth table

  3. Majority Function (a) Truth table for majority function of three variables. (a) A circuit for (a). • M=ABC+ABC+ABC +ABC

  4. Circuit Equivalence • Construction of (a)NOT, (b)AND, and (c)OR gates using only NAND gates or only NOR gates.

  5. Circuit Equivalence (Cont…) • To reduce complexity designers try to reduce no. of gates • Circuit computing same function as original with fewer gates is preferred • Boolean algebra can be valuable • Using Distributive law: AB + AC = A (B+C)

  6. Boolean Algebra Main Identities • To Circuit designers start with a Boolean function and then apply the laws of Boolean algebra to it • In an attempt to find a simpler but equivalent one • From the final function, circuit can be constructed

  7. Alternate Symbols for NAND, NOR, AND, OR • De Morgan’s law suggests an alternative notation, (a) an OR gate is equivalent to the NAND gate with inverted inputs • (b) NOR gate can be drawn with an AND gate with inverted inputs • By negating both forms we arrive at (c) and (d) respectively

  8. XOR, Conversion to NAND Gate Only • (a) The truth table for the XOR function • (b-d) Three circuits for computing it

  9. Circuit Equivalence (Cont…) • Same physical gate can compute different functions, depending on the convention used (a) Electrical characteristics of a device. (b) Positive logic, (c) Negative logic, AND function OR function

  10. Integrated Circuits An SSI chip containing four gates

  11. Multiplexers • An eight-input • multiplexer circuit

  12. Multiplexers (a) An MSI multiplexer. (b) The same multiplexer wired to compute the majority function.

  13. Decoders • A 3-to-8 decoder • circuit

  14. Comparators • A simple 4-bit • comparator • .

  15. Programmable Logic Arrays • A 12-input, 6-output • programmable logic array • The little squares represent fuses that can be burned out • . • .

  16. Shifters A 1-bit left/right shifter

  17. Half Adder (a) A truth table for 1-bit addition (b) A circuit for a half adder

  18. Full Adder (a) Truth table for a full adder (b) Circuit for a full adder

  19. Arithmetic Logic Units • A 1-bit ALU

  20. Arithmetic Logic Units • Eight 1-bit ALU slices connected to make an 8-bit ALU • The enables and invert signals are not shown for simplicity

  21. Clocks (a) A clock (b) The timing diagram for the clock (c) Generation of an asymmetric clock

More Related