T flip-flop as a divide-by-two — flip-flops

exam standardtoggle, and what it is for

Answer

Q⁺ column 0110

Why this example is worth doing

A T flip-flop with T held high toggles every clock, so its output is a square wave at half the clock frequency. Chain n of them and you have a binary counter and a divide-by-2ⁿ. The page shows the timing diagram with the ripple delay visible between stages, which is where asynchronous counters get their reputation — each stage's transition is late by one propagation delay, and the errors accumulate.

Try your own input in the Flip-flops & latches. SR, D, JK and T: characteristic tables, excitation tables and timing diagrams.

How the answer is reached

Output table

Output table — columns T, Q, Q⁺
TQQ⁺
000
011
101
110

Compare with

Open the Flip-flops & latches

This input is entered in the tool itself — it is too rich for a link to carry.

Note:

Notation this page assumes

  • Symbols: · is AND, + is OR, ⊕ is XOR, a prime or an overline is NOT. The field also takes ∧ ∨ ¬ ~ ! & | and the words.
  • Operator precedence, tightest first: NOT, then AND (including juxtaposition), then XOR/XNOR, then NAND/NOR, then OR, then IMPLIES, then IFF.
  • Gate symbols follow whichever standard the header toggle is set to: ANSI/IEEE Std 91-1984 distinctive shapes, or IEC 60617-12 rectangles.

Sources

  • ANSI/IEEE Std 91-1984, Graphic Symbols for Logic Functions
  • IEC 60617-12, Graphical Symbols for Diagrams — Binary Logic Elements