Sequential Logic Circuits

Tom Kelliher, CS26

Oct. 10, 1996



To summarize combinational design, we'll do one or two of the following.

  1. Design and implement a 2-1 multiplexer, using a K-map for minimization of the output equation. Here's the truth table:

    A multiplexer works like a switch. One way of drawing them is:

  2. Design and implement a circuit to take a BCD-encoded digit and drive a seven-segment display (used in watches and calculators). Use a K-map to minimize each of the seven output equations. Take advantage of don't cares. Here is the labeling for the display:

  3. Design and implement a circuit to take a BCD-encoded digit and increment it by one (nine should be ``incremented'' to zero). Use a K-map to minimize each of the four output equations. Take advantage of don't cares.


  1. Sequential circuits.

  2. Combinational circuits have no memory.

  3. Memory provided by feedback --- output becomes input in an ``earlier'' part of the circuit.

  4. Clock signal --- a special control signal used to orchestrate state changes within the circuit. Types of clocked circuits:
    1. Level sensitive --- state changes may occur when the clock signal is at a particular level (0 or 1).

    2. Master-Slave --- The use of two clock signals with pairs of level-sensitive flip-flops to prevent ``double-clocking.'' Suffers from ``ones-catching.''

    3. Edge-triggered --- state changes may occur only on a clock transition (edge).

  5. State --- The values stored by sequential circuit elements (flip-flops, latches). The value of a particular signal.

Types of flip-flops:

  1. R-S. Unclocked R-S:

    Truth table:

    Inputs always sampled --- state changes at any time.

    Timing diagram?

  2. J-K. Clocked (level-sensitive) J-K:

    Truth table:

    Timing diagram?

    Important timing nomenclature:

    1. Propagation delay.

    2. Set-up time.

    3. Hold time.

    Master-slave J-K:

    Timing diagram?

  3. D. Negative edge-triggered D flip-flop:

    Truth table:

    How does it work? Consider:

Multiplexers and Decoders

  1. Multiplexer --- -to-1 switch:

    ``Tiling'' multiple multiplexers to switch words.

  2. Decoder --- 1-of- driver:


  1. Tiling D flip-flops.

  2. Selective loading.

Tying It All Together --- A Register File

The MIPS statement

            add $t0, $t1, $t2
must read two operands and write one in a single cycle.

Need a three-port register file.

General block diagram of register file:

Detailed block diagram:

Thomas P. Kelliher
Wed Oct 9 15:12:30 EDT 1996
Tom Kelliher