$4\mathrm{.}2$ Counters

A counter is a sequential circuit that counts in a particular code $($upwards or downwards$).$ A counter can be realized using all types of FFs $($the additional logic gates need to be changed when you change the FF type, however$).$ Counters for the binary code and the Gray code are already well know from the lecture.

Some properties of a counter:

Counting up means that the number in the next cycle will be higher than the current one

Auto$-$run means that the counter automatically starts when the circuit is powered on$/$the simulation begins

A synchronous counter is a counter where each of the flip$-$flops is connected to one single clock line, that means all flip$-$flop have a common clock line.

For an asynchronous counter, the clock$-$inputs of some flip$-$flops are connected to the outputs of other flip$-$flops, that is$,$ each of the flip$-$flops may have a different clock

$4\mathrm{.}3$ Counter for $5-3-2-1$ code

As circuit diagrams for counters using binary code an Gray code are well known, in this lab a counter using the $5-3-2-1$ code is to be designed.

You already know binary code and Gray code $($lab $2).$ The $5-3-2-1$ code is a $4-$bit code that makes a positional numeral system. The positional values of the $5-3-2-1$ code aren't $2^3,2^2,2$ and $1$ as in the binary code, but $5,3,2$ and $1.$ This is clarified by the following example:

$4-$bit binary code: $,7(dec)=0111=0*2^3+1*2^2+1*2+1*1$

$4-$bit $5-3-2-1$ code : $,7(dec)=1010=1*5+0*3+1*2+0*1$

Q $8$: What is the number $6$ in the $5-3-2-1$ code, what in binary code?