- T Flip Flop Definition: A T flip flop, also known as a toggle flip flop, is defined as a type of flip flop that changes its output state with each clock pulse when its input is high.
- Truth Table: The truth table of a T flip flop shows that the output toggles when T is high and the clock signal is high, otherwise, the output remains unchanged.
- Circuit from JK Flip Flop: A T flip flop can be constructed from a JK flip flop by connecting the J and K inputs together.
- Timing Diagram: The t flip flop timing diagram shows how the output state changes in sync with the input T signal and clock pulses.
- Applications: T flip flops are commonly used in digital counters and frequency dividers due to their toggle feature.
What is a T Flip Flop?
A T flip-flop (toggle flip-flop) has one data input T plus a clock. T = 1 makes the output flip on the active clock event. T = 0 holds the output. The usual build ties both J and K of a JK flip flop to that T pin.
The output is a logic 0 or 1, not a power switch. With T = 1 it complements Q. With T = 0 it holds Q. The next-state rule is Q+ = T XOR Q.
The stored truth table below assumes an active clock. An edge-triggered part (the usual 74-series JK used as a T) updates only on the active clock edge, not for the whole time the clock sits high. A level-sensitive teaching latch would follow T while enable is high. Read the datasheet for the part you have.
The stored symbol is the usual T block with Q and Q-bar. A triangle on the clock pin means edge trigger.
T Flip Flop Truth Table
T is the only data input. A clock (or enable) is still required. The device does not “only work” while the clock is high; it samples on the active event and otherwise holds.
If T = 0 at the capturing clock event, Q stays Q.
If T = 1 at that event, Q becomes the complement of the old Q.
Table-1 is that next-state table. The stored note treats clock as high for every row. Qn is the present state and Qn+1 is the next state after the active clock event.
| T | Qn | Qn+1 | |
| 0 | 0 | 0 | Unchanged/hold |
| 0 | 1 | 1 | Unchanged/hold |
| 1 | 0 | 1 | Toggle |
| 1 | 1 | 0 | Toggle |
T Flip Flop Circuit
A standalone T-only 74-series part is uncommon. The usual method is a dual JK such as MC74HC73A (negative-edge JK with clear): tie J to K and use that node as T.
You can also build T behaviour from SR or D cells with extra gates. Tying J = K is the shortest path.
T Flip Flop Using JK Flip Flop
No extra gates: short J to K and call that pin T.
Use table-1 with the JK excitation table (table-2). X means “don’t care.”
| Qn | Qn+1 | J | K |
| 0 | 0 | 0 | X |
| 0 | 1 | 1 | X |
| 1 | 0 | X | 1 |
| 1 | 1 | X | 0 |
The combined table-3 lists T, present Q, next Q and the J/K values that produce that change.
| T | Qn | Qn+1 | J | K |
| 0 | 0 | 0 | 0 | X |
| 0 | 1 | 1 | X | 0 |
| 1 | 0 | 1 | 1 | X |
| 1 | 1 | 0 | X | 1 |
Map those J and K columns on a K-map.
K-map for J:
![\[ J = T \]](https://www.staging.electrical4u.com/wp-content/ql-cache/quicklatex.com-54318efabcd0a793cce594402f130433_l3.png "Rendered by QuickLaTeX.com")
K-map for K:
![\[ K = T \]](https://www.staging.electrical4u.com/wp-content/ql-cache/quicklatex.com-ef3fefcd0f727d6a92361e05ba439805_l3.png "Rendered by QuickLaTeX.com")
The maps reduce to J = T and K = T, so a common T pin on J and K is a T flip-flop. The stored figure shows that wiring.
T Flip Flop Using SR Flip Flop
The same conversion from a SR Flip flop needs two AND gates, as the maps below show.
Use table-1 and the SR excitation table (labelled table-3 again on this page).
| Qn | Qn+1 | S | R |
| 0 | 0 | 0 | X |
| 0 | 1 | 1 | 0 |
| 1 | 0 | 0 | 1 |
| 1 | 1 | X | 0 |
Combined T-to-SR table:
| T | Qn | Qn+1 | S | R |
| 0 | 0 | 0 | 0 | X |
| 0 | 1 | 1 | X | 0 |
| 1 | 0 | 1 | 1 | 0 |
| 1 | 1 | 0 | 0 | 1 |
K-maps for S and R:
K-map for S:
![\[ S = T Q_{n}' \]](https://www.staging.electrical4u.com/wp-content/ql-cache/quicklatex.com-aec6a46b05521374960cf4e1e710af5d_l3.png "Rendered by QuickLaTeX.com")
K-map for R:
![\[ R = T Q_n \]](https://www.staging.electrical4u.com/wp-content/ql-cache/quicklatex.com-cab8cb55ce348e5b02e76c772b1390f3_l3.png "Rendered by QuickLaTeX.com")
From those expressions, S is T AND Q-bar of the present state, not Qn+1, and R is T AND present Qn.
That is two AND gates into S and R, as in the stored figure.
T Flip Flop Using D Flip Flop
From a D flip flop, D must equal the desired next Q. Use table-1 and the D excitation table.
| Qn | Qn+1 | D |
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
Conversion table: D equals the desired next Q for each T row.
| T | Qn | Qn+1 | D |
| 0 | 0 | 0 | 0 |
| 0 | 1 | 1 | 1 |
| 1 | 0 | 1 | 1 |
| 1 | 1 | 0 | 0 |
K-map for D:
The diagonal grouping is XOR. D in terms of T is the next two stored lines (not “expiration”).
![\[ D = T' Q_n + T Q_n' \]](https://www.staging.electrical4u.com/wp-content/ql-cache/quicklatex.com-81fb9bf49a86c72fb86766be52348248_l3.png "Rendered by QuickLaTeX.com")
![\[ D = T \oplus Q_n \]](https://www.staging.electrical4u.com/wp-content/ql-cache/quicklatex.com-8d56e5d61be87ff9d0d0a46a00402e39_l3.png "Rendered by QuickLaTeX.com")
So D = T XOR Q, which needs one XOR gate in front of D.
The D-to-T figure caption is the line above; this page does not store a separate D-circuit image after it.
T Flip Flop Timing Diagram
T does not toggle “the input.” With T = 1 at the clock event, the output Q toggles.
The stored timing figure starts at T0 with Qn low and Qn+1 (Q-bar) high. Treat the traces as matching that figure.
At the stored T1 mark, T goes low to high. On the figure, Qn and Qn+1 swap, so Qn is high and Qn+1 is low. That matches a toggle if the clock event sits there on the figure.
At T2, T goes high to low. The stored figure holds the outputs.
At T3, T goes low to high again and the figure shows another Qn / Qn+1 swap.
At T4, T goes high to low and the figure holds until T5.
On that figure, T shows two cycles from T1 to T5 while Qn and Qn+1 show one. The usual ÷2 hook-up is T tied high and the signal to divide fed into the clock, not T used as the clock. Both uses rely on the toggle rule.
