--- title: "JK flip-flop with symbol, equation, state diagram" subject: "Digital Logic" chapter: 6 key: "semester_3/digital_logic:jk-flipflop-state-diagram" source: https://www.bctengineer.com/q/semester_3/digital_logic/jk-flipflop-state-diagram site: BCT Engineering --- # JK flip-flop with symbol, equation, state diagram Digital Logic · Chapter 6: Flip Flops - Asked in: 2082 Baisakh, 8 marks - Video: [JK Flip Flop: Circuit, Working, Truth Table, Characteristics Table & Excitation Table](https://www.youtube.com/watch?v=8trVtmPMSbY) — Engineering Funda - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_3/digital_logic/jk-flipflop-state-diagram - Whole chapter: https://www.bctengineer.com/md/semester_3/digital_logic/chapter-6 ## Question Explain the operation of J-K flip-flop with logic diagram, graphic symbol, characteristics table, characteristic equation and state diagram. ## Short answer A JK flip-flop toggles when J=K=1, sets for J=1,K=0, resets for J=0,K=1, and holds for 00. Characteristic equation: Q+ = J Q' + K' Q. The state diagram has two states: 0→1 on 1x, 1→0 on x1; self-loops for 0: 0x, 1: x0. ## Answer A **J-K flip-flop** is an improved S-R flip-flop: J acts like Set, K like Reset, and the input J = K = 1, which is invalid for S-R, makes the output **toggle**. #### Logic diagram (clocked J-K using NAND gates) ```text +------+ S* +------+ J -------| |----->| | CLK -----| NAND | | NAND |-----> Q Q' ------| G1 | Q'->| G3 | +------+ +------+ +------+ R* +------+ K -------| |----->| | CLK -----| NAND | | NAND |-----> Q' Q ------| G2 | Q-->| G4 | +------+ +------+ G3-G4: cross-coupled NAND latch. Q' is fed back to G1 and Q to G2. ``` G1 gets J, CLK and Q'; G2 gets K, CLK and Q; G3-G4 form a NAND latch. In practice the clock is an edge (or master-slave) clock so that the output changes once per clock. #### Graphic symbol ```text +---------+ J ---| J Q |--- Q CLK -|> | K ---| K Q' |--- Q' +---------+ '>' = edge triggered (a bubble 'o>' means negative edge triggered) ``` #### Operation - **J = 0, K = 0:** G1 = G2 = 1, latch holds: no change. - **J = 0, K = 1:** G2 = 0 when Q = 1, latch resets: Q = 0. - **J = 1, K = 0:** G1 = 0 when Q = 0, latch sets: Q = 1. - **J = 1, K = 1:** only the gate with the 1 feedback fires, so the output toggles: Q+ = Q'. - No clock: inputs ignored, output held. #### Characteristic table | J | K | Q | Q+ | |---|---|---|---| | 0 | 0 | 0 | 0 | | 0 | 0 | 1 | 1 | | 0 | 1 | 0 | 0 | | 0 | 1 | 1 | 0 | | 1 | 0 | 0 | 1 | | 1 | 0 | 1 | 1 | | 1 | 1 | 0 | 1 | | 1 | 1 | 1 | 0 | #### Characteristic equation ```text K-map for Q+ (rows Q, columns JK) Q\JK 00 01 11 10 0 0 0 1 1 1 1 0 0 1 Groups: J.Q' (row 0, cells 11,10) K'.Q (row 1, cells 00,10) ``` $$ Q_{n+1} = J\,\overline{Q_n} + \overline{K}\,Q_n $$ #### State diagram The flip-flop has two states, Q = 0 and Q = 1. Each arrow is labelled with the J K inputs that cause that transition at the clock edge (x = don't care): ```text JK = 1x +-------------------------+ | v +-------+ +-------+ | Q = 0 | | Q = 1 | +-------+ +-------+ ^ | +-------------------------+ JK = x1 Self-loop on Q=0: JK = 0x (00 or 01) Self-loop on Q=1: JK = x0 (00 or 10) ``` - From 0: stays 0 for JK = 00 (hold) or 01 (reset); goes to 1 for 10 (set) or 11 (toggle). - From 1: stays 1 for JK = 00 or 10; goes to 0 for 01 or 11. These labels are exactly the excitation table: 0 to 1 needs J = 1, K = x; 1 to 0 needs J = x, K = 1. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What does the J-K flip-flop do for J = K = 1, which is invalid for S-R? A. Holds its state B. Sets Q = 1 C. Toggles: Q+ = Q' D. Resets Q = 0 Answer: C. The J = K = 1 input makes the output toggle. (Key point: J=K=1 toggle) 2. Which is the characteristic equation read from the K-map groups? A. Q+ = J Q' + K' Q B. Q+ = J' Q + K Q' C. Q+ = J K + Q D. Q+ = J Q + K Q' Answer: A. The groups are J.Q' and K'.Q. (Key point: Characteristic equation) 3. Which J K inputs cause the transition from Q = 0 to Q = 1? A. JK = x1 B. JK = 0x C. JK = 1x D. JK = x0 Answer: C. From 0 to 1 needs J = 1, K = don't care (set or toggle). (Key point: State diagram 0 to 1) 4. Which inputs cause the transition from Q = 1 to Q = 0, and which keep it at 1? A. Go to 0 for JK = x1; stay at 1 for JK = x0 B. Go to 0 for JK = x0; stay at 1 for JK = x1 C. Go to 0 for JK = 1x; stay at 1 for JK = 0x D. Go to 0 only for JK = 11 Answer: A. From 1: reset (01) or toggle (11) go to 0, so K = 1; JK = 00 or 10 keeps 1. 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