STEP 1
Below are explanations and work for the circuit involving boolean expressions, truth tables, and K-maps
Truth Table:
This truth table follows the m74 segment pin out having a 1 where that segment would be outputted. Since 0 has A,B,C,D,E, and F highlighted, then all of those segments would have a value of 1 with G being 0 or not lit up. The X, Y, Z values are in ascending order as the binary values increment by 1 at each level. The output column is meant to show the number outputted which corresponds to my birthday. It is also important to note that a "-" has only the G segment light up.
Written Expressions
K-Map Simplification
A:
!X!Y!Z + !X!YZ + X!Y!Z + XY!Z + XYZ ->
!X!Y + XY + !Y!Z
​
B:
!X!Y!Z + !X!YZ + !XYZ + X!Y!Z + XY!Z + XYZ ->
!XZ + !X!Y + XY + X!Z
​
C:
!X!Y!Z + !X!YZ + !XYZ + X!Y!Z + XY!Z + XYZ ->
!XZ + !X!Y + XY + X!Z
​
D:
!X!Y!Z + XY!Z ->
!X!Y!Z + XY!Z
​
E:
!X!Y!Z + XY!Z ->
!X!Y!Z + XY!Z
​
F:
!X!Y!Z + X!Y!Z + XY!Z ->
X!Z + !Y!Z
​
G:
!XY!Z + X!Y!Z + X!YZ ->
X!Y + !XY!Z
