ECE 101 An Introduction to Information

Technology

Digital Logic

Information Path

InformationDisplay

Information Processor

& Transmitter

InformationReceiver and

Processor

Source ofInformation

DigitalSensor

TransmissionMedium

Combinational Logic Gates

• Fundamental Gates

• Exclusive OR

• Seven Segment Displays

• Binary Addition

• Binary Subtraction– 2’s complement notation

Fundamental Logic GatesAND GateUse a dot to indicate the AND operation

A NAND =

_

Y=A·B not AND = Y

B NOT =

_A B Y=A·B Y

0 0 0 1 0 1 0 1 1 0 0 1 1 1 1 0

Y_Y

Fundamental Logic GatesOR GateUse a plus sign to indicate the OR operation NOR gate A _

Y=A+B = not OR = Y B

_A B Y=A+B Y

0 0 0 1 0 1 1 0 1 0 1 0 1 1 1 0

A

B

_Y

Combinational Logic Gates• N input variables yields 2N possible inputs

– A truth table lists output for all possible combinations of input variables

– Combinational Logic Gates implement a truth table

• Given a binary pattern b3 b2 b1 b0

– Implement with AND gate, so transform all given inputs into a set of 1’s since the union will give a one.

Combinational Logic Gates

• Examples– Implement a circuit to produce a 6– Implement a circuit to produce a 13

• More than one pattern, use Y = pattern 1 + pattern 2 + … pattern N– Implement a circuit to implement either a 6 or

14

Combinational Logic Gates

• Fundamental Gates

• Exclusive OR

• Seven Segment Displays

• Binary Addition

• Binary Subtraction– 2’s complement notation

Seven segment displays

Truth Table to convert BCD codes to 7- segment display

Logic circuit for the letter “a” to be displayed

Binary Adder Truth Table

Binary Adder, Sum bit

Binary Subtraction• Subtracting a number is the same as adding

the negative of the number 14-9=14+(-9)=5• Use 2’s complement notation to get the

negative number• First complement all the bits in the number• Then add one• 1310 = 011012 find –13 by 2’s complement:• Complement each bit 10010 • And add one: +00001• To get 10011 the value of –13• Add this now to 13 to get 00000

Sequential Logic Circuits• Depend upon past and present input values

– Combinatorial: use truth tables– Sequential: use timing diagrams

• Most common sequential logic circuits include “flip-flops”, each is capable of storing one bit of information.

• “set-reset flip-flop”: basic computer memory cell

• “toggle flip-flop”: basic computer counting cell

Set-Reset Flip-Flop• Computer’s basic memory cell• Implemented by two OR gates and two Not

gates (or two NOR gates) that use feedback (connection of output to input).

• Two inputs: S, set and R, reset and two outputs, Q and not Q

• Note Q remembers whether S or R was “one” last – this is the memory capability of SRFF

S-R flip-flop

Addressable Memory• Uses both combinatorial and sequential

logic• Random access memory (RAM) stores and

retrieves binary data as needed• Each cell or memory location has a unique

address• At the S input there is an AND gate with the

address & input data• At the R input there is another AND gate

with complement of the input data and the address

Addressable Memory

• In order to be stored at a memory location the address signal must be 1 then the output of the memory (SRFF) is the DATA input value.

• To retrieve the contents of the memory cell the out put is connected to an AND cell again with the address signal.

• Hence the output of the AND occurs only when the address is 1

Toggle flip-flop

Toggle Flip-Flop• Basic computer counting cell

• Two inputs, a toggle (T) and clear (C), and one output Q

• The value of Q changes (or toggles) when when ever a 1 to 0 transition occurs at the input T

• When a 1 appears at the C input, the Q resets to 0 and remains at 0 as long as C=1.

Binary Counting with T F-F

Note the error here: “14” should be “13”.

Toggle Flip-Flop• As a result, Q has twice the period (or ½ the

number of pulses) as T

• By cascading a series of n, T-FF, and connecting to each output, a counter can be made up to 2n – 1.

Modulo-N Counter

• A counter uses a chain of T-FFs

• Recall M T-FFs count from 0 to 2M - 1

• Modulus (mod) of a counter is the number of counting states before it repeats itself

• If we wish a counter that is not 0 to 2M – 1, then we must apply a clear (C) at some point to start the counting over again.

Modulo-6 Counter

Digital Clock

• 7 segment display

• Counts 60 Hz frequency of ac power line

• Use of mod 60 to get to minutes from seconds

• Use of mod 10 to get to 10 minute digits

• Use of mod 6 to get to hours

• Use of mod 12 to reset the clock