Lecture 9: Sequential Logic & Storage

1. Combinational vs. Sequential Circuits

• Combinational: Output depends only on current inputs (e.g., Decoders, Adders). No memory.
• Sequential: Output depends on current inputs AND the previous state (memory).

2. Latches (Asynchronous)

• The simplest memory element. It uses feedback.
• S-R Latch:
  • $S=1, R=0 \rightarrow$ Set ($Q=1$).
  • $S=0, R=1 \rightarrow$ Reset ($Q=0$).
  • $S=0, R=0 \rightarrow$ Memory (No change).
  • $S=1, R=1 \rightarrow$ Invalid/Forbidden state.

3. Flip-Flops (Synchronous)

• Unlike latches, they change state only on a Clock signal (Edge-triggered).
• JK Flip-Flop: Fixes the SR latch problem. If $J=1$ and $K=1$, the output Toggles (flips from 0 to 1 or 1 to 0).

4. Binary Counters

• Built from a series of flip-flops. Each flip-flop represents 1 bit.
• Function: Counts the number of clock pulses in binary.
• Applications: Digital clocks, timers, and frequency dividers.