APS 非重点复习课程之数字逻辑

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