3-bit ripple counter from T flip-flops

edge casethe first sequential system

Answer

Q2⁺ column 00011110, Q1⁺ column 01100110, Q0⁺ column 10101010

Why this example is worth doing

Three toggle flip-flops in a chain count from zero to seven and wrap. The page uses it to close the sequential section with a complete system rather than a component, and to expose the ripple problem honestly: because each stage clocks the next, the outputs are briefly inconsistent after every transition, and decoding them combinationally produces glitches. That is the argument for synchronous counters, which is where the next course starts.

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 Q2, Q1, Q0, Q2⁺, Q1⁺, Q0⁺
Q2Q1Q0Q2⁺Q1⁺Q0⁺
000001
001010
010011
011100
100101
101110
110111
111000

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