ECE 275: Digital Design I
Class 9Design Problems
- Three switches (A, B, C) trigger F when at least 2 switches are on
| A | B | C | F |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 1 | 1 | 1 |
| 1 | 0 | 0 | 0 |
| 1 | 0 | 1 | 1 |
| 1 | 1 | 0 | 1 |
| 1 | 1 | 1 | 1 |
F = A'BC + AB'C + ABC' + ABC + ABC + ABC F = AB(C + C') + BC(A + A') + AC(B + B') F = AB + BC + AC
- Three Switches (A, B, C) trigger F when ABC >= 3
| A | B | C | F |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 1 | 1 | 1 |
| 1 | 0 | 0 | 1 |
| 1 | 0 | 1 | 1 |
| 1 | 1 | 0 | 1 |
| 1 | 1 | 1 | 1 |
F = A'BC + AB'C' + AB'C + ABC' + ABC F = A'BC + AB'C' + AB'C + AB F = A'BC + AB' + AB F = A'BC + A F = A + BC
- Three Switches (A, B, C) trigger F when decimal of ABC is evenly divisible by 2
| A | B | C | F |
|---|---|---|---|
| 0 | 0 | 0 | 1 |
| 0 | 0 | 1 | 0 |
| 0 | 1 | 0 | 1 |
| 0 | 1 | 1 | 0 |
| 1 | 0 | 0 | 1 |
| 1 | 0 | 1 | 0 |
| 1 | 1 | 0 | 1 |
| 1 | 1 | 1 | 0 |
F = A'B'C' + A'BC' + AB'C' + ABC' F = C'(A'B' + A'B + AB' + AB) F = C'(A' + A) F = C'
More Gates
- AND *
- OR +
- NOT '
- XOR ⊕ u2295
- XNOR ⊙ (Equivalence Gate) u2299
Larger Circuits
Half Adder
Adds two bits
A + B = S carry C
| A | B | S | C |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 0 | 1 | 1 | 0 |
| 1 | 0 | 1 | 0 |
| 1 | 1 | 0 | 1 |
S = A ⊕ B C = AB
Full Adder
Adds three bits
| A | B | Cin | S | Cout |
|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 1 | 0 |
| 0 | 1 | 0 | 1 | 0 |
| 0 | 1 | 1 | 0 | 1 |
| 1 | 0 | 0 | 1 | 0 |
| 1 | 0 | 1 | 0 | 1 |
| 1 | 1 | 0 | 0 | 1 |
| 1 | 1 | 1 | 1 | 1 |
S = B ⊕ C