[Digital Logic] Flip-Flop | 플립플롭

Flip-Flop

플립플롭

---

S-R Flip-Flop (S-R 플립플롭)

S-R Flip-Flop Characteristic Table

S	R	Q(t+1)
0	0	No Change
0	1	0
1	0	1
1	1	Indeterminate

 

---

JK Flip-Flop (JK 플립플롭)

* J : Jam
* K : Kill

JK Flip-Flop Symbol & State Diagram

JK Flip-Flop Behavioral Table

J	K	Q(t)	Q(t+1)	Description
0	0	0	0	Hold
0	0	1	1
0	1	0	0	Reset
0	1	1	0
1	0	0	1	Set
1	0	1	1
1	1	0	1	Toggle
1	1	1	0

JK Flip-Flop Characteristic Table

J	K	Q(t+1)
0	0	Q(t)
0	1	0
1	0	1
1	1	Q'(t)

JK Flip-Flop State Equation
\(Q(t+1) = J'K'Q(t) + JK' + JKQ'(t) + JQ' + K'Q\)

JK Flip-Flop Timing Diagram Example

---

D Flip-Flop (D 플립플롭; Delay)

* D FFs: Delay FFs
- Input을 한 Cycle만큼 Delay시켜서 출력하는 FFs이다.
- 즉, Input을 그대로 출력하는, Buffer와 비슷한 역할을 한다.

D Flip-Flop Symbol & State Diagram

D Flip-Flop Characteristic Table

D	Q(t+1)
0	0 (Reset)
1	1 (Set)

D Flip-Flop State Equation
\(Q(t+1) = D\)

---

Example. Sequential Circuit using a D-FF

1) State Equation (Transition Equation)
A(t+1) = A \oplus x \oplus y

2) State Table (Transition Table)

Present State	Inputs		Next State
A	x	y	A(t+1)
0	0	0	0
0	0	1	1
0	1	0	1
0	1	1	0
1	0	0	1
1	0	1	0
1	1	0	0
1	1	1	1

3) State Diagram (Transition Diagram)

---

Example. Sequential Circuit using D-FFs

1) State Equation (Transition Equation)

\(A(t+1) = Ax + Bx\)
\(B(t+1) = A'x\)
\(y(t+1) = (A+B)x'\)

2) State Table (Transition Table)

Present State		Input	Next State		Output
A	B	x	A	B	y
0	0	0	0	0	0
0	0	1	0	1	0
0	1	0	0	0	1
0	1	1	1	1	0
1	0	0	0	0	1
1	0	1	1	0	0
1	1	0	0	0	1
1	1	1	1	0	0

3) State Diagram (Transition Diagram)

---

T Flip-Flop (T 플립플롭; Toggle)

T Flip-Flop Symbol & State Diagram

T Flip-Flop Characteristic Table

T	Q(t+1)
0	Q(t) (No Change)
1	Q'(t) (Complement)

T Flip-Flop State Equation
\(Q(t+1) = T \oplus Q = T'Q + TQ'\)

T Flip-Flop Timing Diagram Example

---

Excitation Table (여기표)

- Present State에서의 Q(t) 값에서 Next State의 Q(t+1)으로 변화한 값을 통해,
  변화를 일으킨 Input 값을 유추한 테이블이다.

---

JK Flip-Flop Excitation Table

Q(t)	Q(t+1)	J	K
0	0	0	X
0	1	1	X
1	0	X	1
1	1	X	0

1) Q(t)=0 \to Q(t+1)=0
- Q(t+1) = Q(t)인 경우, JK = 00
- Q(t+1) = 0인 경우, JK = 01
\therefore JK = 0X

2) Q(t)=0 \to Q(t+1)=1
- Q(t+1) = 1인 경우, JK = 10
- Q(t+1) = Q'(t)인 경우, JK = 11
\threrfore JK = 1X

3) Q(t)=1 \to Q(t+1)=0
- Q(t+1) = 0인 경우, JK = 01
- Q(t+1) = Q'(t)인 경우, JK = 11
\threrfore JK = X1

4) Q(t)=1 \to Q(t+1)=1
- Q(t+1) = Q(t)인 경우, JK = 00
- Q(t+1) = 1인 경우, JK = 10
\threrfore JK = X0


* JK Flip-Flop Characteristic Table

J	K	Q(t+1)
0	0	Q(t)
0	1	0
1	0	1
1	1	Q'(t)

* Example. Synthesis using JK FFs

---

T Flip-Flop Excitation Table

Q(t)	Q(t+1)	T
0	0	0
0	1	1
1	0	1
1	1	0

1) Q(t)=0 \to Q(t+1)=0
- Q(t+1) = Q(t)인 경우, T = 0

2) Q(t)=0 \to Q(t+1)=1
- Q(t+1) = Q'(t)인 경우, T = 1

3) Q(t)=1 \to Q(t+1)=0
- Q(t+1) = Q'(t)인 경우, T = 1

4) Q(t)=1 \to Q(t+1)=1
- Q(t+1) = Q(t)인 경우, T = 0

TFlip-Flop Characteristic Table

T	Q(t+1)
0	Q(t) (No Change)
1	Q'(t) (Complement)