Chapter Summary

Chapter 10 — Digital Electronics develops digital circuits in two halves. The combinational half (covered in the earlier parts of the chapter) deals with logic gates — including the XOR and XNOR gates and the universal NAND and NOR gates — digital codes (BCD, gray, excess-3, ASCII, EBCDIC), arithmetic building blocks such as the half adder, full adder and half subtractor, Boolean simplification using min-terms and max-terms, the SOP and POS forms and the Karnaugh map, and the realization of expressions using AND–OR and NAND–NAND logic.

The sequential half, summarized here, rests on memory:

• Sequential vs combinational. A combinational circuit's output depends only on its present inputs (no memory); a sequential circuit's output depends on present and past inputs, so it needs memory elements fed back around a combinational block. A clock — a periodic train of pulses with defined rising and falling edges — synchronizes these updates, and flip-flops respond either on a clock edge (positive or negative) or on a level.
• Flip-flops. A flip-flop is a bistable element storing one bit, with complementary outputs $Q$ and $\overline{Q}$. The SR latch (cross-coupled NAND gates) has SET, RESET, HOLD and an INVALID state; the D flip-flop removes the invalid state by making its inputs complementary, so $Q$ follows D; the JK flip-flop restores all four modes and adds TOGGLE, using $S = J\cdot\overline{Q}_n$ and $R = K\cdot Q_n$; the race-around problem when J=K=1 is cured by the Master-Slave JK flip-flop, which sets the Master on the rising edge and delivers the Slave output on the falling edge; and the T (toggle) flip-flop is a JK with J=K=1 that complements its output once per clock pulse. Flip-flops are used for data storage, transfer, frequency division, counting and serial/parallel conversion.
• Registers. A register is a set of flip-flops storing binary data; a shift register takes its data in serially. The four modes are SISO, SIPO, PISO and PIPO, differing in whether data enters and leaves serially or in parallel. Shift registers serve as storage and flag registers, delay lines, ring counters and serial/parallel converters (the UART). …