Homework 4 Boolean Reduction solution

Instructions



The inputs for the reduction will be:




S0 = Current State 0th bit (least signi cant) S1 = Current State 1st bit (most signi cant) G = Valid card scan from card scanner




F = Gate sensor: whether or not there is a car under the gate Your outputs for the reduction will be:




N0 = Next State 0th bit (least signi cant) N1 = Next State 1st bit (most signi cant) A = Scan Card Now light at the kiosk




B = Signal to the motor to keep the gate open C = Signal to the motor to keep the gate closed




1.1 State Machine Diagram




The diagram below represents the behavior of the state machine. For more information, refer to the assignment document.










State 1




Gate Open




B




G F












State 0


State 2
start
Gate Closed
!F
Car in Gate


AC
B

























1












Truth Table



2.1 Instructions




For all combinations of the inputs G, F, S1, and S0, ll in the corresponding outputs of the state machine.




This State Machine is a Moore State Machine, meaning the output values are determined solely by the current state (that is, you should not use the N1 and N0 outputs for determining the values for A; B; C.) Use the character 'x' to denote don't care states.




G
F
S1
S0


N1
N0
A
B
C




















0
0
0
0
































0
0
0
1
































0
0
1
0
































0
0
1
1
































0
1
0
0
































0
1
0
1
































0
1
1
0
































0
1
1
1
































1
0
0
0
































1
0
0
1
































1
0
1
0
































1
0
1
1
































1
1
0
0
































1
1
0
1
































1
1
1
0
































1
1
1
1



































CHECKPOINT: Go on Canvas and submit your truth table in the Home-work 4 Worksheet Contents assignment. Check your score and make any corrections necessary. You can submit as many times as you want.






















2












K-Maps



For each K-Map, ll in the appropriate gray codes as column and row headers and perform the groupings for each output. You MUST show the groupings! Try using di erent colored pens/pencils to make it easier to read.




(a) K-Map for N1 (b) K-Map for N1




S1S0
00




10


S1S0
00




10
GF










GF






























00










00










































































10










10






























(a) K-Map for A




(b) K-Map for B












S1S0
00




10


S1S0
00




10
GF










GF






























00










00










































































10










10







































(a) K-Map for C







S1S0 00
10
GF




00










10





































3












Reduced Expressions



Now use the K-maps to write down the reduced expressions.




N1 =







N0 =







=






=






=









Submit



Complete the following steps:




Enter all of your K-Map and Reduced Expression work into the Home-work 4 Worksheet Contents assignment on Canvas. For information on how to enter your reduced expressions, see below.



Once that's done, scan this document and submit the scan, with all of the pages, onto the Homework 4 Worksheet Scan assignment on Grade-scope. This will be used during the demo.



The following is the formatting requirement for your reduced boolean expres-sions (not following these will get you penalized).




Use apostrophe (') to denote negation. e.g. if you have an expression where F is 0, denote this with F', not !F.



Your expressions should be ordered from longest term to shortest term. For example, if you have the terms S0 and GF S1S0, write the nal ex-pression as GFS1S0+S0, since GFS1S0 is a longer term.



Each term should be ordered G F S1 S0. So GFS1 would be valid, but S1FG would not.



In the case of two terms of same length, break ties "alphabetically" where the "alphabet" is GF S1S0. So between FS1 and GS0, you would write GS0+FS1 because G is higher priority.



Don't put any spaces in the expressions: write f+g and not f + g.



You need to submit on BOTH platforms!










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