qunatum gate

Quantum Computing — Study Notes

Single Qubit Gates

Complete Reference Guide for Students

📄 Topic 3.1

⏱️ ~45 min read

📑 Table of Contents

1. What is a Qubit?

8. Quick Reference Table

2. What are Quantum Gates?

9. Bloch Sphere Visualization

3. Pauli-X Gate

10. Important Relationships

4. Pauli-Y Gate

11. Worked Example

5. Pauli-Z Gate

12. Key Takeaways

6. Hadamard Gate

13. Common Exam Questions

7. Phase Gates (S & T)

14. Rotation Gates (Rx, Ry, Rz)

01 What is a Qubit?

A qubit is the fundamental unit of quantum information. Unlike a classical bit (which is either 0 or 1), a qubit can exist in a superposition of both states simultaneously.

$$|\psi\rangle = \alpha|0\rangle + \beta|1\rangle$$

Where:

• $\alpha, \beta \in \mathbb{C}$ are complex numbers called probability amplitudes
• $|\alpha|^2 + |\beta|^2 = 1$ — the normalization condition (total probability = 1)

📐 Column Vector Representation

$$|0\rangle = \begin{pmatrix} 1 \\ 0 \end{pmatrix}, \qquad |1\rangle = \begin{pmatrix} 0 \\ 1 \end{pmatrix}$$

Any qubit state can be written as: $|\psi\rangle = \begin{pmatrix} \alpha \\ \beta \end{pmatrix}$

02 What are Quantum Gates?

Property	Classical Gates	Quantum Gates
Reversibility	Reversible or Irreversible	Always Reversible
Operates on	Classical bits	Qubits
Representation	Truth tables	Unitary Matrices
Determinism	Can be non-deterministic	Always deterministic

KEY PROPERTY — Unitarity

$$U^\dagger U = UU^\dagger = I$$

Where $U^\dagger$ is the conjugate transpose (adjoint) of $U$, and $I$ is the identity matrix.

🔄

Reversible

Every gate has inverse

📏

Norm-Preserving

Output always valid

🎯

Deterministic

Same input → same output

03 Pauli-X Gate NOT Gate Bit Flip

The Pauli-X gate is the quantum equivalent of the classical NOT gate. It flips the state of a qubit: $|0\rangle \leftrightarrow |1\rangle$.

$$X = \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}$$

Action on |0⟩

$$X|0\rangle = \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}\begin{pmatrix} 1 \\ 0 \end{pmatrix} = \begin{pmatrix} 0 \\ 1 \end{pmatrix} = |1\rangle$$

Action on |1⟩

$$X|1\rangle = \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}\begin{pmatrix} 0 \\ 1 \end{pmatrix} = \begin{pmatrix} 1 \\ 0 \end{pmatrix} = |0\rangle$$

💡 Bloch Sphere: X gate rotates the state by 180° around the X-axis.

Self-inverse: $X^2 = I$, so $X^{-1} = X$

04 Pauli-Y Gate Bit + Phase Flip

The Pauli-Y gate combines a bit flip with a phase flip, introducing imaginary numbers.

$$Y = \begin{pmatrix} 0 & -i \\ i & 0 \end{pmatrix}$$

Action on |0⟩

$$Y|0\rangle = i|1\rangle$$

Action on |1⟩

$$Y|1\rangle = -i|0\rangle$$

🎯 Bloch Sphere: Rotates by 180° around the Y-axis. Self-inverse: $Y^{-1} = Y$

05 Pauli-Z Gate Phase Flip

The Pauli-Z gate leaves $|0\rangle$ unchanged but flips the phase of $|1\rangle$ by multiplying it by $-1$.

$$Z = \begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix}$$

Action on |0⟩

$$Z|0\rangle = |0\rangle \quad \text{(unchanged)}$$

Action on |1⟩

$$Z|1\rangle = -|1\rangle \quad \text{(phase flipped)}$$

⚠️ Important: Z does NOT change measurement probabilities!

$|\alpha|^2$ and $|\beta|^2$ remain the same — only the relative phase changes.

06 Hadamard Gate Most Important Superposition

The Hadamard gate is the most commonly used gate in quantum computing. It creates an equal superposition of $|0\rangle$ and $|1\rangle$.

$$H = \frac{1}{\sqrt{2}}\begin{pmatrix} 1 & 1 \\ 1 & -1 \end{pmatrix}$$

H|0⟩ = |+⟩

$$H|0\rangle = \frac{|0\rangle + |1\rangle}{\sqrt{2}} = |+\rangle$$

Equal superposition (positive phase)

H|1⟩ = |−⟩

$$H|1\rangle = \frac{|0\rangle - |1\rangle}{\sqrt{2}} = |-\rangle$$

Equal superposition (negative phase)

Key Properties of H Gate:

Property	Expression
Self-inverse	$H = H^\dagger = H^{-1}$
Double application	$H^2 = I$
Conjugation: X → Z	$HXH = Z$
Conjugation: Z → X	$HZH = X$
Basis switch	Converts between Z-basis and X-basis

💡 Bloch Sphere: H rotates 180° around the axis halfway between X and Z (the X+Z diagonal axis).

07 Phase Gates (S & T)

S Gate π/2 Phase

$$S = \begin{pmatrix} 1 & 0 \\ 0 & i \end{pmatrix}$$

$S|0\rangle = |0\rangle$

$S|1\rangle = i|1\rangle$

Key: $S^2 = Z$, $S^\dagger = \begin{pmatrix} 1 & 0 \\ 0 & -i \end{pmatrix}$

T Gate π/4 Phase

$$T = \begin{pmatrix} 1 & 0 \\ 0 & e^{i\pi/4} \end{pmatrix}$$

$T|0\rangle = |0\rangle$

$T|1\rangle = e^{i\pi/4}|1\rangle$

Key: $T^2 = S$, $T^4 = Z$

🔗 Phase Gate Hierarchy:

$$T \xrightarrow{T^2} S \xrightarrow{S^2} Z$$

Applying T twice gives S. Applying S twice gives Z. Applying T four times gives Z.

14 Rotation Gates (R_x, R_y, R_z)

Rotation gates allow arbitrary-angle rotations around each axis of the Bloch sphere. They are the most general single-qubit gates.

R_x(θ)

Around X-axis

$$\begin{pmatrix} \cos\frac{\theta}{2} & -i\sin\frac{\theta}{2} \\ -i\sin\frac{\theta}{2} & \cos\frac{\theta}{2} \end{pmatrix}$$

R_y(θ)

Around Y-axis

$$\begin{pmatrix} \cos\frac{\theta}{2} & -\sin\frac{\theta}{2} \\ \sin\frac{\theta}{2} & \cos\frac{\theta}{2} \end{pmatrix}$$

R_z(θ)

Around Z-axis

$$\begin{pmatrix} e^{-i\theta/2} & 0 \\ 0 & e^{i\theta/2} \end{pmatrix}$$

Special Cases:

Rotation	Equivalent To	Note
$R_x(\pi)$	$X$ (with global phase)	180° around X
$R_y(\pi)$	$Y$ (with global phase)	180° around Y
$R_z(\pi)$	$Z$ (with global phase)	180° around Z
$R_z(\pi/2)$	$S$ (with global phase)	90° around Z
$R_z(\pi/4)$	$T$ (with global phase)	45° around Z

08 Quick Reference Table

Gate	Matrix	Key Action	Self-Inverse?
I	$\begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}$	Identity (nothing)	✅ Yes
X	$\begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}$	Bit flip (NOT)	✅ Yes
Y	$\begin{pmatrix} 0 & -i \\ i & 0 \end{pmatrix}$	Bit + Phase flip	✅ Yes
Z	$\begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix}$	Phase flip	✅ Yes
H	$\frac{1}{\sqrt{2}}\begin{pmatrix} 1 & 1 \\ 1 & -1 \end{pmatrix}$	Superposition	✅ Yes
S	$\begin{pmatrix} 1 & 0 \\ 0 & i \end{pmatrix}$	π/2 phase shift	❌ No ($S^\dagger$)
T	$\begin{pmatrix} 1 & 0 \\ 0 & e^{i\pi/4} \end{pmatrix}$	π/4 phase shift	❌ No ($T^\dagger$)

09 Bloch Sphere Visualization

Every single-qubit state (up to a global phase) can be represented as a point on the Bloch Sphere:

$$|\psi\rangle = \cos\frac{\theta}{2}|0\rangle + e^{i\phi}\sin\frac{\theta}{2}|1\rangle$$

Parameter	Range	Description
θ	$[0, \pi]$	Polar angle from Z-axis (|0⟩)
φ	$[0, 2\pi)$	Azimuthal angle from X-axis in XY-plane

Key States on Bloch Sphere:

• North Pole: $|0\rangle$ — θ=0

• South Pole: $|1\rangle$ — θ=π

• +X axis: $|+\rangle$ — θ=π/2, φ=0

• −X axis: $|-\rangle$ — θ=π/2, φ=π

• +Y axis: $|{+i}\rangle$ — θ=π/2, φ=π/2

• −Y axis: $|{-i}\rangle$ — θ=π/2, φ=3π/2

Gate	Rotation Axis	Angle
X	X-axis	180° (π)
Y	Y-axis	180° (π)
Z	Z-axis	180° (π)
H	X+Z diagonal axis	180° (π)
S	Z-axis	90° (π/2)
T	Z-axis	45° (π/4)

10 Important Relationships to Remember

🔄 Inverse Gates

$X^{-1} = X$

$Y^{-1} = Y$

$Z^{-1} = Z$

$H^{-1} = H$

$S^{-1} = S^\dagger = \begin{pmatrix} 1 & 0 \\ 0 & -i \end{pmatrix}$

$T^{-1} = T^\dagger = \begin{pmatrix} 1 & 0 \\ 0 & e^{-i\pi/4} \end{pmatrix}$

🔗 Useful Identities

$HXH = Z$

$HZH = X$

$S^2 = Z$

$T^2 = S$

$T^4 = Z$

$H^2 = I$

✖️ Pauli Multiplication Rules

$$XY = iZ$$

$$YZ = iX$$

$$ZX = iY$$

⚠️ Note: $XY \neq YX$ — Pauli matrices do not commute! (anti-commutation: $\{X,Y\} = 0$)

11 Worked Example

❓ Problem: Apply H gate followed by Z gate to |0⟩

Step 1: Apply H to |0⟩

$$H|0\rangle = \frac{1}{\sqrt{2}}\begin{pmatrix} 1 & 1 \\ 1 & -1 \end{pmatrix}\begin{pmatrix} 1 \\ 0 \end{pmatrix} = \frac{1}{\sqrt{2}}\begin{pmatrix} 1 \\ 1 \end{pmatrix} = \frac{|0\rangle + |1\rangle}{\sqrt{2}} = |+\rangle$$

Step 2: Apply Z to the result

$$Z \cdot H|0\rangle = Z\left(\frac{|0\rangle + |1\rangle}{\sqrt{2}}\right) = \frac{Z|0\rangle + Z|1\rangle}{\sqrt{2}} = \frac{|0\rangle - |1\rangle}{\sqrt{2}} = |-\rangle$$

✅ Final Answer:

$$ZH|0\rangle = |-\rangle = \frac{|0\rangle - |1\rangle}{\sqrt{2}}$$

💡 Alternative: Using Matrix Multiplication

Combine into single matrix: $ZH = \begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix}\frac{1}{\sqrt{2}}\begin{pmatrix} 1 & 1 \\ 1 & -1 \end{pmatrix} = \frac{1}{\sqrt{2}}\begin{pmatrix} 1 & 1 \\ -1 & 1 \end{pmatrix}$

12 Key Takeaways

✅ Single qubit gates = 2×2 unitary matrices. Every gate must satisfy $U^\dagger U = I$.

✅ Pauli gates (X, Y, Z) are the fundamental building blocks — they rotate by 180° around their respective axes.

✅ Hadamard (H) creates equal superposition — the most frequently used gate in quantum algorithms.

✅ Phase gates (S, T) add relative phases between |0⟩ and |1⟩ without changing measurement probabilities.

✅ Rotation gates (Rx, Ry, Rz) allow arbitrary-angle rotations — any single-qubit operation can be decomposed into these.

✅ All quantum gates are reversible — this is a key difference from classical computing (e.g., NAND gate is not reversible).

✅ Bloch sphere is the geometric tool to visualize single-qubit states and understand gate actions as rotations.

✅ Global phases are physically irrelevant — only relative phases between |0⟩ and |1⟩ matter.

13 Common Exam Question Types

1 Matrix Multiplication

"Apply gate G to state |ψ⟩" → Write state as column vector, multiply by gate matrix.

💡 Tip: Always write the gate matrix on the LEFT, state vector on the RIGHT: G|ψ⟩

2 Sequential Gate Application

"What state results from applying H then X then Z to |0⟩?" → Multiply matrices right to left.

⚠️ Common mistake: For $G_3 G_2 G_1 |\psi\rangle$, multiply $G_3 \times G_2 \times G_1$ (right to left), NOT left to right!

3 Prove Unitarity

"Show that the Hadamard gate is unitary" → Compute $H^\dagger H$ and show it equals $I$.

💡 Tip: For real matrices, $U^\dagger = U^T$ (just transpose). For complex matrices, also conjugate each entry.

4 Gate Decomposition

"Express the S gate in terms of Z and T" → Use identities like $T^2 = S$ or $S^2 = Z$.

5 Bloch Sphere Analysis

"What rotation does the H gate perform?" → Identify the axis and angle of rotation on the Bloch sphere.

6 Measurement Probabilities

"What are the measurement probabilities after applying H to |0⟩?" → Square the absolute values of amplitudes.

💡 Example: $H|0\rangle = \frac{1}{\sqrt{2}}|0\rangle + \frac{1}{\sqrt{2}}|1\rangle$ → P(0) = $|\frac{1}{\sqrt{2}}|^2$ = 0.5, P(1) = $|\frac{1}{\sqrt{2}}|^2$ = 0.5

🌟 PRO TIP — Order of Matrix Multiplication

For a circuit: |0⟩ —[G₁]—[G₂]—[G₃]— |ψ⟩

The mathematical expression is: $|\psi\rangle = G_3 \cdot G_2 \cdot G_1 \cdot |0\rangle$

Think of it as: the rightmost gate acts first on the state, just like function composition: $f(g(h(x)))$ means h acts first.

Quantum Computing — Single Qubit Gates

Study Notes • Topic 3.1 • 📚

Latex code -Template

SKCET Presentation Template

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SKCET-Presentation Template	Template set file and model file
Latex -software installation	Miketex and Texstudio
MCQ Generation guide	MCQ Generation guide

Qunatum Computing Questions

Quantum computing

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Model Questions	Model Questions

Question bank

Quantum computing

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Model Questions	Lab Questions

Quantum Computing - Book chapter Calls

Call for Book Chapters

"Exploring Hardware Advances: FPGA, IoT, Microcontrollers, and Quantum Technologies"

We invite original submissions for chapters exploring cutting-edge developments in FPGA, IoT, Microcontrollers, and Quantum Technologies. Contributions from researchers, engineers, academicians, practitioners, and industry experts are welcome to showcase the latest breakthroughs and their impact on society. Contributions may encompass theoretical frameworks, case studies, experimental findings, and practical insights. We encourage submissions that address the intersection of hardware advancements with fields such as artificial intelligence, robotics, cybersecurity, healthcare, and beyond.

The hardware kits that could be used for the application, but are not limited to:

• Microcontroller Development Kits: Arduino Boards, Raspberry Pi, STM32 Discovery Boards, PIC Microcontroller Starter Kits
• FPGA Development Kits: Xilinx Zynq and Spartan Boards, Altera (now part of Intel) FPGA Boards, Lattice Semiconductor FPGA Boards
• IoT Development Kits: ESP8266 and ESP32 Development Boards, Particle Photon and Electron, Feather Boards
• Machine Learning and AI Kits: NVIDIA Jetson Developer Kits, Google Coral Development Board, Intel Movidius Neural Compute Stick
• Wireless Communication Kits: Nordic Semiconductor nRF52/nRF51 Development Kits, Texas Instruments CC3XXX & CC13XXX LaunchPads, Zigbee and Z-Wave Development Kits
• Power Electronics Development Kits: TI Power Supply Design Kits, Analog Devices Power Management Kits, Infineon Power Evaluation Boards
• Analog and Digital Design Kits: Analog Devices ADALM-PLUTO, TI Analog Discovery Kits, Diligent Analog Discovery Boards
• Robotics Kits: LEGO Mindstorms, Raspberry Pi Robotics Kits, Arduino-based Robot Kits
• Sensor Development Kits: Adafruit and SparkFun Sensor Kits, Bosch Sensor Development Kits, STMicroelectronics SensorTile Kits
• Educational Kits: LittleBits Kits, Snap Circuits Kits, Kano Computer Kits

The applications that could be implemented, but are not limited to:

• Wearable devices
• Medical diagnostics
• Remote patient monitoring
• Smart cities, infrastructure & monitoring
• Traffic management systems
• Smart grid optimization
• Communication and networking
• Cryptography algorithms
• Communication protocols
• Wireless sensor networks
• Manufacturing & Industrial Automation
• Environmental Monitoring and Sustainability
• Energy-efficient systems
• Quantum computing algorithms
• Quantum communication & cryptography
• Quantum sensing and metrology

Book Editors:

• Manikandan Veerappan, Assistant Professor, Department of Computer Science and Engineering, School of Computing, Kalasalingam Academy of Research and Education, Krishnankoil, Srivilliputhur, India
• Professor Sardar M.N. Islam, Professor, Institute for Sustainable Industries and Liveable Cities, Victoria University, Melbourne, Australia
• Mubarak Ali, SoC Digital Designer, Engineering and Research Services, HCLTech, Chennai, India

Author Benefits:

There are no fees for processing or publication. The primary author of each chapter will be given a complimentary copy of the book upon publication.

Submission Guidelines:

Authors are invited to submit a chapter proposal (abstract) outlining the topic, objectives, methodology, and intended contribution (300-500 words) to the email address profmani@acm.org. The subject of the email should be ‘ELSEVIER_EHA_2024’.

Submissions should be original and not under consideration for publication elsewhere. All submissions will undergo a rigorous peer-review process to ensure quality and relevance.

Important Dates:

• Proposal Submission Deadline: October 30, 2024
• Notification of Proposal Acceptance: November 10, 2024
• Full Chapter Submission Deadline: January 06, 2025
• Final Notification of Acceptance: February 03, 2025

Further instructions for the full chapter submission will be communicated once the chapter proposal is accepted. Any queries or issues can be addressed to the editors through email at profmani@acm.org, with the subject line "EHA_query".

Micro computing Systems

Content	Link
Module 1	Module 1- 8086 Notes
Module 1	8086 -Memory management -notes
Module 1	8086 Architecture -Power point
Module 1	8086 Instruction set and addressing mode -PPT
Module 1	ARM processor PPT
Module 1	ARM processor PPT
Module 2	8051 Controller ppt
Module 2	8051 Controller ppt
Queastion Bank	Question bank CIA 1
Queastion Bank	Question bank CIA 1 Part A Answer

Latex- Beamer - Title page -sec 1

  
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Assending order of ALP model of 8086 processor

  ORG 100h        ; Origin at 100h

MOV SI, OFFSET NUMBERS ; SI points to the array of numbers
MOV CX, 5       ; Number of elements to sort (change as needed)

SORT_LOOP:
    MOV BX, CX      ; Inner loop counter
    DEC BX          ; Decrement BX since we compare BX with BX+1

INNER_LOOP:
    MOV AX, [SI]    ; Load the value at SI into AX
    CMP AX, [SI+2]  ; Compare with the next value
    JLE NO_SWAP     ; Jump if less than or equal (no swap needed)

    ; Swap the values
    XCHG AX, [SI+2]
    MOV [SI], AX

NO_SWAP:
    ADD SI, 2       ; Move to the next element
    LOOP INNER_LOOP ; Repeat for all elements

    DEC CX          ; Decrement outer loop counter
    LOOP SORT_LOOP  ; Repeat for all elements

   

NUMBERS DB 23, 11, 56, 7, 34 ; Array of numbers to sort

END
  

Memory Address		Object code				Mnemonics				Comment
4100				74,08					MOV A,# DATA 1			Move DATA 1 to A
4102				75,F0,04				MOV B,# DATA 2			Move DATA 2 to B
4105				A4					DIVA,B					Divide A and B
4106				90,00,45				MOV DPTR,#4500			Move 4500 to DPTR
4109				F0						MOVX @DPTR,A			Move A to DPTR
410A				A3						INC DPTR				Increment DPTR
410B				E5,F0					MOV A,B					Move B to A
410D				F0						MOVX @DPTR,A			Move A to DPTR
410F				80,FE					SJMP 410F				End

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\geometry{a4paper} % or letterpaper (US) or a5paper or....
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Latex source code template- Answer Key

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% These packages are optional, depending whether you want the features they provide.
% See the LaTeX Companion or other references for full information.

%%% PAGE DIMENSIONS
\usepackage{geometry} % to change the page dimensions
\geometry{a4paper} % or letterpaper (US) or a5paper or....
\geometry{margin=1.0in} % for example, change the margins to 2 inches all round
% \geometry{landscape} % set up the page for landscape
%   read geometry.pdf for detailed page layout information

\usepackage{graphicx} % support the \includegraphics command and options
\usepackage{sidecap}% for figure in sides
\usepackage{wrapfig}

%package for page border
\usepackage[export]{adjustbox}

%watermark
\usepackage{draftwatermark}% water mark
\SetWatermarkText{SKCT} %

\SetWatermarkScale{3}
\usepackage[parfill]{parskip} % Activate to begin paragraphs with an empty line rather than an indent

%%% PACKAGES
\usepackage{hyperref}
\usepackage{booktabs} % for much better looking tables
\usepackage{array} % for better arrays (eg matrices) in maths
\usepackage{paralist} % very flexible & customisable lists (eg. enumerate/itemize, etc.)
\usepackage{verbatim} % adds environment for commenting out blocks of text & for better verbatim
\usepackage{float}
\usepackage{tikz}
\usetikzlibrary{shapes.geometric, arrows}

\usepackage{color, colortbl}
% circut package for elctrical and electronics circuit draws
%\usepackage{circuitikz}
\usepackage[siunitx]{circuitikz}
%\usepackage{xcolor}
%\usepackage{subfig} % make it possible to include more than one captioned figure/table in a single float
\usepackage{amsmath}
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\usepackage[normalem]{ulem}
\useunder{\uline}{\ul}{}
\usepackage{caption}
\usepackage{subcaption}
\usepackage{wrapfig}
\setlength{\parindent}{4em}
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\lfoot{By Dr.PR,Dr.KS,Dr CS, Ms.MP, Mr MN, }\cfoot{SKCT}\rfoot{\thepage}

%%% SECTION TITLE APPEARANCE
\usepackage{sectsty}
\allsectionsfont{\sffamily\mdseries\upshape} % (See the fntguide.pdf for font help)
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\usepackage[nottoc,notlof,notlot]{tocbibind} % Put the bibliography in the ToC
\usepackage[titles,subfigure]{tocloft} % Alter the style of the Table of Contents
\renewcommand{\cftsecfont}{\rmfamily\mdseries\upshape}
\renewcommand{\cftsecpagefont}{\rmfamily\mdseries\upshape} % No bold!
\usepackage{setspace} % line space package

%\usepackage[table,xcdraw]{xcolor}
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        \usepackage{siunitx}
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        \usepackage{pdfpages}
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%8086 program 
\usepackage{listings}
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	xleftmargin=\parindent,
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%8086 program end
        
\begin{document}
	
	\begin{table}[h!]
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			\raisebox{-\totalheight}{\includegraphics[width=0.1\textwidth, height=20mm]{Presentation/ski}}
			
			& 
		\begin{center}
			\begin{large}
				\textbf{Sri Krishna College of Technology(Autonomous), Coimbatore }
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			  NACC  and NBA accredited \\
			\begin{large}
			\textbf{Department of ECE }
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			\end{tabular}
		\end{center}
	\end{table}
	

\begin{flushleft}
	\textbf{Staff :Dr.P.Rajasekar Dr.K.Shanthi, Dr.C.SenthilKumar Ms.M.Priyadharshini	Mr.M.Navinkumar\\ 
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		Subject :Microprocessors and Micro controllers                  \hspace{5mm}              Course Code :21IT502 }
\end{flushleft}
\begin{center}
	\begin{large}
	Question Bank
	\end{large}
\end{center}


 \end{document}

Microprocessor 8086

Content	Link
Notes	Assembler Directives
Notes	8086 Introdcution, pin configuration, Minimum mode, maximum mode, addressing mode