$[$Please refer to the attached image$]$

At your first job after grathating, you have been assigned to design the logic circuit of a

new childreris toy. The toy is furned on by the parent using a small button on the back

that is not part of your design. Once the ficy is tumed on$,$ there are $2$ large buttons on

the front that the child may press. You must cansider both of these buttons in your

design.

Button $1$ controls the lighting of $3$ lights: red, yellow, and blue. Before button $1$ is

pressed, the toy is in its inifial state with no lights on$.$ When button $1$ is first pressed, the

red light tums on$.$ When button $1$ is pressed again, the red light turns off and the yellow

light immedately turns on$.$ Wher buton $1$ is pressed again, the yelow light lums of and

the blue light immedstely turns on$.$ When button $1$ is pressed again, the blue light turns

off and the red light immedately turns on again. There are $3$ culputs from your circuit

connecting to the lights. One output goes to each of the $3$ lights. You must send a logic

high signal to the appropriate light to turn it on$.$

The second button controk music played by the toy. Pegardess of what state the lights

are in$,$ a press of bution $2$ turns the music on$.$ When the music is on$,$ a press of bution $2$

turns the music off. There is $1$ oulput from your circuit cornecting to the music player.

This oulput should be logic high wher the music is onc. You may assume orly $1$ buthon is

pressed at a fime. The button press is momentary, where one press geverales a $1$ in

the incorring serial data inputs, which are otherwise $0.$ If your design results in unused

states, ensure their next state is off. Any culputs from unused states are to be treated

as off for their value. Implement your design for the lights and music using. JK llip$-$flops

in a Moore model On the following pages you will find $5$ parts to this question which will

require you to daw the state dagram, define the state table, minimize the Boclean

functions, nestly draw the final circuit, and modity the design.

a$)$ Very neatly and concisely draw the state diagram$($s$)$ for this design. Be sure

to desrly labed states, imput$($s$),$ and oulput$($s$).$ Clearly defire each state and

assign each an appropriate binary value. $[5$ marks$]$

b$)$ Very neatly record the correct crdered state table$($s$)$ of the state diagram and

inclute the fip$-$flop inputs. $[5$ marks$]$

c$)$ Neatly create and complete the required k$-$maps for the design and minimize

the minterns. Place a bow around each firal minimized Boolean function.

Ensure to write each term in alphabetical order $($i$.$e$.,$ correct porst, incorrect:

stqpr$).[5$ maks$]$

d$)$ Very neatly daw your design's digtal circuit using standard logic symbols.

Label all inputs and outpus You may assume the complement of any

variable is rearily available. $[6$ marks$]$

e$)$ Now imagine the design specification has changed slightly so that the music

is only turned on by button $2$ i a light is on$.$ For example, if no light is on$,$ a

press of button $2$ will not have ary effect. Use JK flip$-$lops in a Moore model.

Draw the new cigital circuit. You do not need to do the full design process if

you can otherwise determine a correct circuit that will implement the required

functionaity. Labed al inputs and outputs. You may assume the complement

of any yariable is regdy