3: Logic Gates
- Page ID
- 899
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
\( \newcommand{\dsum}{\displaystyle\sum\limits} \)
\( \newcommand{\dint}{\displaystyle\int\limits} \)
\( \newcommand{\dlim}{\displaystyle\lim\limits} \)
\( \newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\)
( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\id}{\mathrm{id}}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\kernel}{\mathrm{null}\,}\)
\( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\)
\( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\)
\( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\AA}{\unicode[.8,0]{x212B}}\)
\( \newcommand{\vectorA}[1]{\vec{#1}} % arrow\)
\( \newcommand{\vectorAt}[1]{\vec{\text{#1}}} % arrow\)
\( \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vectorC}[1]{\textbf{#1}} \)
\( \newcommand{\vectorD}[1]{\overrightarrow{#1}} \)
\( \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} \)
\( \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} \)
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\(\newcommand{\longvect}{\overrightarrow}\)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)- 3.1: Digital Signals and Gates
- This page examines the use of binary numeration in electronics, particularly within digital circuits, highlighting the representation of binary bits as voltage signals in transistors. It covers important aspects such as the function of logic gates that amplify these binary signals, their schematic representations, input configurations, and truth tables.
- 3.2: The NOT Gate
- This page covers advanced inverter circuit design using transistors and diodes, highlighting its enhanced performance and reliability compared to single-transistor models. It explains the circuit's operation with input states and the impact of steering diodes on current flow for binary outputs, noting TTL characteristics.
- 3.3: The “Buffer” Gate
- This page explains how connecting two inverter gates in series cancels their inversion, functioning as a signal amplifier without altering logic levels. This role is fulfilled by buffers, represented by a triangle symbol, which boost current capacity for load driving. Buffers can have open-collector or totem pole outputs. Their internal mechanisms, utilizing transistors, determine the output state based on the input, preserving the logic relationship while enhancing signal strength.
- 3.4: Multiple-input Gates
- This page covers the functionality and principles of various logic gates, including AND, OR, NAND, NOR, Exclusive-OR, and Exclusive-NOR, with their truth tables and operational principles. It highlights how multiple input terminals enhance the complexity of logic operations and explains output conditions based on input combinations. The importance of these gates in logic circuits for tasks such as bit comparison and error detection is also emphasized, supported by examples of gate behavior.
- 3.5: TTL NAND and AND gates
- This page explains a modified open-collector inverter circuit functioning as a NAND gate, where grounding either input produces a "high" output, while both inputs being high results in a "low" output. It notes that an additional inverter stage can convert this setup into an AND gate, and summarizes the interrelationships among NAND and AND gates in TTL design.
- 3.6: TTL NOR and OR gates
- This page explains a TTL circuit with transistors Q1, Q2, Q3, and Q4 acting as steering networks for inputs A and B, functioning as a NOR gate that outputs high only when both inputs are low. A high input causes the corresponding transistor to saturate, leading to a low output. To convert the NOR gate to an OR gate, an inverter is required at the output. It also mentions the use of totem-pole output stages in both circuit types.
- 3.7: CMOS Gate Circuitry
- This page compares TTL and CMOS logic gates, highlighting their power consumption, design simplicity, and performance. TTL gates maintain consistent power but require constant current, while CMOS gates are more efficient at static states and allow for greater voltage range and fanout, though they are sensitive to static voltages and slower due to high input capacitance.
- 3.8: Special-output Gates
- This page covers complementary output gates, tristate gates, and bilateral switches. Complementary output gates deliver both inverted and non-inverted outputs, enhancing circuit efficiency. Tristate gates can output various states, controlled by an enable input, while bilateral switches act as solid-state relays using MOSFETs to manage electrical signals. The discussion emphasizes the functional benefits of these specialized gates in diverse electronic applications.
- 3.9: Gate Universality
- This page discusses the universal nature of NAND and NOR gates, capable of replicating any logic gate through strategic connections. It explains constructing basic logic functions, including inverters, buffers, and variations of AND and OR gates, and emphasizes the transformation of functions via input inversion (DeMorgan's Theorem). Ultimately, it highlights the importance of NAND and NOR gates as essential components in digital control systems.
- 3.10: Logic Signal Voltage Levels
- This page explains the operation and compatibility of TTL and CMOS logic gates at 5V, noting their noise margins and signal state definitions. It emphasizes the challenges in mixed systems and the importance of using proper interfacing methods to ensure reliable signal interpretation.
- 3.11: DIP Gate Packaging
- This page discusses digital logic gate circuits, detailing their integration using transistors and resistors on semiconductors within DIP housings, which vary in pin counts. It explains the significance of part numbers like “74LS02” for identifying gate types, with variants from different manufacturers.


