1 / 19

# Building Functions from Logic Gates - PowerPoint PPT Presentation

Building Functions from Logic Gates. We've already seen how to implement truth tables using AND, OR, and NOT -- an example of combinational logic . Combinational Logic Circuit output depends only on the current inputs stateless Sequential Logic Circuit

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about 'Building Functions from Logic Gates' - liluye

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.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

• We've already seen how to implement truth tablesusing AND, OR, and NOT -- an example of combinational logic.

• 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.

Consider computing 7+6=13:

A combinational logic design

Now, consider one column of this addition:

Truth table for a 1-bit adder:

Formulate a circuit for each output

The Majority Circuit for CarryOut

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

• A device with multiple inputs and 1 output

• Could be used to allocate a resource to one of multiple clients:

• A 2n-to-1 multiplexer (MUX) sends one of 2n input lines to a single output line

• A MUX has two sets of inputs:

• 2n data input lines

• n select lines used to pick one of the 2n data inputs

• Simplest example is a 2-to-1 MUX

• n-bit selector and 2n inputs, one output

• output equals one of the inputs, depending on selector

00

01

10

11

4-to-1 MUX

• General example:

• Assume that some information is encoded in n bits

• For each encoding, we want to activate the (one) correct output line

• The general idea: given an n-bit input

• Detect which of the 2n combinations is represented

• Produce 2n output, only one of which is “1”

• A n-to-2n decoder takes an n-bit input and produces 2n outputs. The n inputs represent a binary number that determines which one of the 2n outputs is “true” (i.e., 1).

This circuit decodes a binary input into one of four possible choices, or codes

• n inputs, 2n outputs

• exactly one output is 1 for each possible input pattern

2-bit

decoder

• Number bits from right (0) to left (n-1)

• just a convention -- could be left to right, but must be consistent

• Use brackets to denote range:D[l:r] denotes bit l to bit r, from left to right

• May also see A<14:9>, especially in hardware block diagrams.

0

15

A = 0101001101010101

A[2:0] = 101

A[14:9] = 101001

Multibit Values in Circuit Diagrams

• A 4-to-1 mux, selecting one byte out of a 32-bit value...

• Combinational Circuit

• always gives the same output for a given set of inputs

• ex: adder always generates sum and carry,regardless of previous inputs

• Sequential Circuit

• stores information

• output depends on stored information (state) plus input

• so a given input might produce different outputs,depending on the stored information

• example: ticket counter

• advances when you push the button

• output depends on previous state

• useful for building “memory” elements and “state machines”