Using the requirements and equipment given please complete $1-4$:

$1)$A function table of D Flip Flop containing both present state Q and next state Q$+$;

$2)$State table for complete operation $($A table contains input x$,$present states of C$/$B$/$A$,$next states

of C$/$B$/$A$,$output z$,$and present D Flip Flop inputs D$2,$D$1,$and D$0)$;

$3)$K$-$maps to obtain Boolean equations of D$2,$D$1,$D$0$and z$,$and the application of DeMorgan$$s to convert them into NAND gate and AND gate formats;

$4)$Built a circuit diagram

EQUIPMENT REQUIRED:

Global Specialties Design and Prototyping PB$-505$A

Wire Leads

$1$ Logic Probe

$27400$ TTL quad two input NAND gate integrated circuit chip

$17408$ TTL quad two input AND integrated circuit chip

$17410$ TTL triple three input NAND integrated circuit chip

$174175$ TTL Quad D Flip$-$Flop

LAB INTRODUCTION:

Design a counter which has one input, x$,$ and four outputs, C$,$B$,$A$,$ and z$.$ Output signals C$,$B$,$ and A are

three D Flip$-$Flop outputs $($ Q$\_(2),$Q$\_(1)$ and Q$\_(0))$ which form a three$-$bit binary number with C as the most significant

bit $($MSB$)$ and A as the least significant bit $($LSB$).$ This binary number will be displayed as a digit on one of the

$7-$segment LED displays on the PB$-505$A Digital Lab. Note that the flip$-$flop outputs are labeled C$,$ B$,$ A$,$ to

match the inputs of the $7-$segment LED display on the PB$-505$A $($as shown in Fig$\mathrm{.}1).$

When x$=1$ the digit should progress through the sequence $0,1,2,3,4,5,$ and remain at $5$

when it is reached. State transitions should occur on the clock pulse. You should determine when

such transitions will occur $($i$.$e$.,$ rising or falling edge of the clock pulse$).$ The output z should equal $1$

only when the counter has reached five AND while x$=1.$

If$,$ at any time, x is changed to a $0,$ the next digit which appears with the next clock pulse should

be a zero. The input x and the clock should be controlled by a logic switch.

quad The output z should control a logic monitor.

quad All unused states $(110,111)$ should transition to the $000$ state on the first clock pulse.