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Boolean Algebra, Logic Gates, Truth Tables, De Morgan's Law

Some are simple, such as those in flashlights. Others, such as those used in supercomputers, are extremely complex. This collection of modules takes the topic of electric circuits a step beyond simple circuits. When the circuit is purely resistive, everything in this module applies to both DC and AC. Matters become more complex when capacitance is involved. We do consider what happens when capacitors are connected to DC voltage sources, but the interaction of capacitors and other nonresistive devices with AC is left for a later chapter. Finally, a number of important DC instruments, such as meters that measure voltage and current, are covered in this chapter.

Figures (10)

A logic circuit diagram for a 4-bit carry lookahead binary adder design using only the AND, OR, and XOR logic gates
A synchronous 4-bit up/down decade counter symbol (74LS192) in accordance with ANSI/IEEE Std 91-1984 and IEC Publication 60617-12 [missing "C3" at pin 11]
Circuit diagram: NOR(NOR(NOR(A, A), NOR(B, B)), NOR(A, B))
Circuit diagram: NAND(NAND(NAND(A, A), NAND(B, B)), NAND(A, B))
CMOS diagram of a NOT gate, also known as an inverter. MOSFETs are the most common way to make logic gates.
4-to-1 multiplexer
Figure 2. Venn diagrams for conjunction, disjunction, and complement
Animation of how an SR NOR gate latch works
The 7400 chip, containing four NANDs. The two additional pins supply power (+5 V) and connect the ground.
Figure 21.1 Electric circuits in computers and servers allow large amounts of data to be quickly and accurately analyzed. (credit: WOCinTech Chat/Flickr)

Key Points

  • Boolean algebra is therefore a formal way of describing logical operations in the same way that elementary algebra describes numerical operations.
  • Compound logic gates AND-OR-invert (AOI) and OR-AND-invert (OAI) are often employed in circuit design because their construction using MOSFETs is simpler and more efficient than the sum of the individual gates.
  • Truth tables are also used to specify the function of hardware look-up tables (LUTs) in digital logic circuitry.
  • A NAND gate is equivalent to an OR gate with negated inputs, and a NOR gate is equivalent to an AND gate with negated inputs.
  • Consider the simplified case where a two-input NAND gate is used to drive a motor when either of its inputs are brought low by a switch.
  • In contrast, the output from combinational logic is purely a combination of its present inputs, unaffected by the previous input and output states.

Terms

Tap a term for a plain-language explanation.

Sources & licensing(4)