1 / 15

Chapter 3 Digital Logic Structures

Chapter 3 Digital Logic Structures. Basic Logic Gates. Basic Relations of Boolean Algebra. x + 0 = x x + 1 = 1 x + x = x x + x ’ = 1 x + y = y + x (Commutative) x + (y+z) = (x+y)+z (Associative) x  (y+z ’ ) = x  y + x  z (Distributive) (x+y) ’ = x ’ y ’ (DeMorgan) (x ’ ) ’ = x.

bevan
Download Presentation

Chapter 3 Digital Logic Structures

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. Chapter 3Digital LogicStructures

  2. Basic Logic Gates

  3. Basic Relations of Boolean Algebra • x + 0 = x • x + 1 = 1 • x + x = x • x + x’ = 1 • x + y = y + x (Commutative) • x + (y+z) = (x+y)+z (Associative) • x(y+z’) = xy + xz (Distributive) • (x+y)’ = x’ y’ (DeMorgan) • (x’)’ = x • x0 = 0 • x1 = x • xx = x • xx’ = 0 • xy = yx (Commutative) • x(yz) = (xy)z (Associative) • x+yz = (x+y)(x+z) (Distributive) • (xy)’ = x’+y’(DeMorgan) + = OR = AND ‘ = NOT

  4. = = DeMorgan’s Law • not(A and B) = (not A) or (not B) • not(A or B) = (not A) and (not B)

  5. More than 2 Inputs? • AND/OR can take any number of inputs. • AND = 1 if all inputs are 1. • OR = 1 if any input is 1. • Similar for NAND/NOR. • Can implement with multiple two-input gates,or with single CMOS circuit.

  6. Summary • MOS transistors are used as switches to implementlogic functions. • n-type: connect to GND, turn on (with 1) to pull down to 0 • p-type: connect to +2.9V, turn on (with 0) to pull up to 1 • Basic gates: NOT, NOR, NAND • Logic functions are usually expressed with AND, OR, and NOT • DeMorgan's Law • Convert AND to OR (and vice versa) by inverting inputs and output

  7. Building Functions from Logic Gates • Combinational Logic Circuit • output depends only on the current inputs • stateless • Sequential Logic Circuit • output depends on the sequence of inputs (past and present) • stores information (state) from past inputs • We'll first look at some useful combinational circuits,then show how to use sequential circuits to store information.

  8. Decoder • n inputs, 2n outputs • exactly one output is 1 for each possible input pattern 2-bit decoder

  9. Multiplexer (MUX) • n-bit selector and 2n inputs, one output • output equals one of the inputs, depending on selector 4-to-1 MUX

  10. A B C D S0 S1 A B C D Out S[1:0] Out Mux (cont.) • In general, a MUX has • 2n data inputs • n select (or control) lines • and 1 output. • It behaves like a channel selector. A 4-to-1 MUX: Out takes the value of A,B, C or D depending on the value of S (00, 01, 10, 11)

  11. Adder • Half Adder • 2 inputs • 2 outputs: sum and carry • Full Adder • performs the addition in column i • 3 inputs: ai, bi and ci • 2 outputs: si and ci+1 • ci is the carry in from bit position i-1 • ci+1 is the carry out to bit position i+1 Half-adder truth table

  12. Full Adder • Add two bits and carry-in,produce one-bit sum and carry-out.

  13. Full Adder (cont) where - verify that this corresponds to the gate-level implementation.

  14. Four-bit Adder 1010 Cin 0101 A + 1101 B 10010 S

  15. Logical Completeness • Can implement ANY truth table with AND, OR, NOT. 1. AND combinations that yield a "1" in the truth table. 2. OR the resultsof the AND gates.

More Related