fe counters topic 3

8/12/2019 FE Counters Topic 3

1/9

Topic 3 Counters

At the end of this section you should be able to:

Describe the use of feedback to make a D-type flop-flip divide bytwo.

Convert a four-bit binary number into decimal or HEX notation.

Desi n !-bit up or down counters based on risin ed e tri eredD-type flip-flops.

Desi n !-bit modulo-" counters and draw timin dia rams.

Describe the use off a #CD or HEX decoder with a sevense ment display.

Counters

Latches can act as a memory for binary numbers that have been put into them.Eight flip-flops can act as a memory for an eight-bit word , or a single byte . Incomputers, which work with bytes, each eight-bit number stands for something,be it a letter, a number, or a character, determined by the ASCII code , universalfor all computers.

Counters are special memories that store a word that represents the number ofpulses that have passed into the circuit. The D-type flip-flop is the simplest

counter for bit.

The timing diagram shows the behaviour of the circuit!


2/9

Question 1 . "hat do you notice about the output compared to the input#ANSWER

This circuit can count two bits!

"hen the reset is made high, the outputs $ go to give a two bit word %& ''. Thecircuit then changes state on the falling edge of the clock pulse, according to thefollowing table!

Pulse B A

' ' '

'

( '
http://www.antonine-education.co.uk/Electronics_AS/Electronics_Mod2/topic_2_3/answer_2_3_01.htmhttp://www.antonine-education.co.uk/Electronics_AS/Electronics_Mod2/topic_2_3/answer_2_3_01.htm


3/9

)

* ' '

The word %& tells us the number of pulses that have arrived. % is the mostsignific nt bit worth ( + ( , while & is the !e st signific nt bit worth ( ' + .

o %& represents ( / 0 / ). The timing diagram is like this!

Question " "hat do you notice about the output trace %# ANSWER

#i$ide by " Circuit


4/9

&s well as acting as a single bit counter, the circuit above, which is a D-type flip-flop with feedback, acts as a di$ide by two circuit . If we look at the timingdiagram, we can see that the number of output pulses is half the number of clockpulses.

Question 3 "hen does the output trace change state# ANSWER

The circuit works like this!

The output $-bar is when $ is '. 1n the first rising edge, $ changes to .

&nd stays there as the clock pulse falls to '.

Then on the ne/t clock pulse, the rising edge causes the output to changeto '.

The output changes every other clock pulse.


5/9

%in ry nd &e' decim ! Counting

2omputers work on bin ry numbers, which mean numbers to the b se " . "e

normally count in tens, because we have ten digits on our front and hind paws.This is b se 1( or decim ! . "e can count in any base we like. In the 34 thecurrency was run on a duodecimal system, counting in base twelve. shilling

( old pence5 pound (' shillings.

"hen we e/press a number, we start off with the most signific nt bit at the lefthand side, and the !e st signific nt at the right. 2onsider the number (*6!

Hundreds Tens Units

Powers of Ten '(

' ''

Number ( * 6

( / '' * / ' 6 /

o (*6 is the sum of ('' 0 *' 0 6

"e do a similar thing in bin ry . The least significant bit is ( ' + , followed by( + ( , followed by ( ( + * , etc. "e will look at a four bit number!

Eight Four Two Units

7owers ofTwo

( ) ( ( ( ( '

8umber '

/ 9 ' / * / ( /

o ' 9 0 ' 0 ( 0 .

Try Question )

2omputer memories are designed to act rather like a set of pigeonholes, orlockers, in which data is posted. Each location has a uni:ue address, which isgiven a number in base ; + ( * , called a *e' decim ! or &E+ code.
http://www.antonine-education.co.uk/Electronics_AS/Electronics_Mod2/topic_2_3/Question_2_3_4.htmhttp://www.antonine-education.co.uk/Electronics_AS/Electronics_Mod2/topic_2_3/Question_2_3_4.htm


6/9

The first < he/adecimal numbers are like the first < decimal numbers. Thecharacter ' represents decimal ;. o there have to be alternative charactersfor decimal ', , (, ), *, and 6. These are &, %, 2, D, E, and =respectively. The table shows decimal numbers ' to ; with their four bit binaryand he/adecimal codes!

Decimal

Four-bitbinary

He a- decimal

' '''' '

'''

( '' ' (

) '' )

* ' '' *

6 ' ' 6

; ' ' ;

> ' >

9 ''' 9

< ''

fe counters topic 3

Documents