1. Introduction to the 1st theoretic Exercise
7-Segment
Introduction to the 1st theoretic Exercise

2. 7 segment – Decimal Digit
When building a digital clock, we’ll probably want to use a 7-segment electrical digit as “GUI”.
How does each segment know when to be turned on?
תירגול 2 - מבנה מחשב

3. 7 Segment – Decimal Digit
The range is 0..9, and since the number of states is 10, we only need 4 bits.
In general, in order to represent n states, we’ll need bits.
0000
0001 1
0010 2
0011 3
0100 4
0101 5
0110 6
0111 7
1000 8
1001 9
תירגול 2 - מבנה מחשב

4. Segment f Example Segment f is on in digits 0, 4, 5, 6, 8, 9.
We’ll build its truth table.
0000
0001 1
0010 2
0011 3
0100 4
0101 5
0110 6
0111 7
1000 8
1001 9
תירגול 2 - מבנה מחשב

5. Segment f Example (2) Seg. f A B C D # 1 2 3 4 5 6 7 8 9 X … 15 00002 3 4 5 6 7 8 9 X … 15
0000
0001 1
0010 2
0011 3
0100 4
0101 5
0110 6
0111 7
1000 8
1001 9
תירגול 2 - מבנה מחשב

6. Segment f Example (3)
Seg. f A B C D # 1 2 3 4 5 6 7 8 9 X … 15
Solution 1: Karnaugh map representation and simplification
Solution 2: Extract DNF, arithmetic simplification
תירגול 2 - מבנה מחשב

7. Segment f Example - Karnaugh
Seg. f A B C D # 1 2 3 4 5 6 7 8 9 X … 15 00 01 11 10 1 X 00 01 11 10
תירגול 2 - מבנה מחשב

8. Segment f Example - DNF (1)
Seg. f A B C D # 1 2 3 4 5 6 7 8 9 X … 15
Ideally we would add to the DNF the beneficial values for the X lines
In practice we will take all X as 0 (for your benefit)
תירגול 2 - מבנה מחשב

9. Segment f Example - DNF (2)00 01 11 10
Not taking the X lines at there “ideal” values yields a less efficient result
Using the same truth table will yield the following Karnaugh map 00 1 01 11 10
תירגול 2 - מבנה מחשב

10. Homework (Theoretical 1)
In the following instructions use the above digital representation.
Perform segment e using arithmetic logical simplification (DNF with 0 instead of X)
Solve segments a-e,g using Karnaugh Maps
Draw the graphical representation for segment c.
notice that only 1 line is allowed to exit a gate !
Use the “full dot” to symbol a branch in a line
Use the “empty dot” to symbol a NOT on an input to another gate.
Use only AND, OR and NOT gates
Submit the papers to your TA in class only! Deadlines:
Groups 3,4:
Group 5:
Groups 6,7:
Exercises without name, ID and group number won’t be checked.
תירגול 2 - מבנה מחשב