Number System
Decimal, binary, octal, hexadecimal (how to transfer)
Logic Operation
and or not nand(与非) nor(或非) xor(异或)
Boolean Function
\(Y=A\overline B+\overline AB+\overline B\overline C+AC\)
Karnaugh Map
simplify the Boolean function.
| A\BC | 00 | 01 | 11 | 10 |
|---|---|---|---|---|
| 0 | 1 | 1 | 1 | |
| 1 | 1 | 1 | 1 |
Adjacent 2 '1' can be merged
result is not only.
both \(\overline A\overline C+A\overline B+BC\) and \(\overline AB+AC+\overline B\overline C\) are correct.
SR Latch
aka Set-reset Latch. detail
| \(S_D\) | \(R_D\) | state(determined by Q) |
|---|---|---|
| 1 | 0 | 1 |
| 0 | 1 | 0 |
| 0 | 0 | keep the state unchanged |
JK flip-flop
synchronous timing circuit. vending machines. detail
\(Q_{next}=J\overline Q+\overline KQ\)
Characteristic Table
| J | K | Comment | Qnext |
|---|---|---|---|
| 0 | 0 | Hold state | Q |
| 0 | 1 | Reset | 0 |
| 1 | 0 | Set | 1 |
| 1 | 1 | Toggle | Q |
Excitation Table
| Q | Qnext | Comment | J | K |
|---|---|---|---|---|
| 0 | 0 | No change | 0 | X |
| 0 | 1 | Set | 1 | X |
| 1 | 0 | Reset | X | 1 |
| 1 | 1 | No change | X | 0 |