Bits & pieces - Sven Wehrend

01_boolean_algebra

Wed, 23 Dec 2020 00:00:00 +0000

Boolean Algebra and Basic Logic Gates

We are starting (the journey) with three very basic logic functions (or operations), which despite their simplicity already are valid instructions of a regular CPU:

NOT, AND and OR

Logical functions - also called operations, the author will use both terms interchangebly here - can be described in various ways, most often it is described implicit as boolean equation, but it can also be explained explicit in a truth table.

How does a CPU work? Overview

Sun, 20 Dec 2020 00:00:00 +0000

== How does a CPU work – Table of Contents

Introduction and Overview

Introduction and Overview

Each topic in this course is divided into two parts: one focusing on the mathematical side of digital logic— ideally independent of implementation details— and another more concrete part dealing with those very details. In the concrete part, we will mostly discuss implementations on the electrical level, although other solutions are possible, such as those based on fluid dynamics or optical gates.

How does a CPU work 2? Overview

Sun, 14 May 2023 00:00:00 +0000

How does a CPU work 2 - Table of contents

From Combinatorial to Sequential Logic - Introduction

Introduction to Sequential Logic

We get from purely conmbinatorial logic circuits wihout any form of memeory to sequential logic circuits with some type of memory (mostly flipflops)

Clocks,Flipflops and registers

Clocks,flipflops and registers

We make a leap into the area of sequential logic and introduce some concepts vital for the sequential logics, like clock, flipflops and registers

02_XOR

Mon, 08 Nov 2021 00:00:00 +0000

== XOR

As there are a lot of important applications for the exclusive-or (XOR) operation it is dedicated an own blog post. Two of the most important are:

XOR operations are often used in a Linear Feedback Shift Registers (LFSR). LFSR are a crucial step in scrambler / descrambler respectively, which are used in transmitters / receivers
Part of an encryption algorithmus
Last but not least an important part of a halfadder.

03_binary_system

Thu, 02 Dec 2021 00:00:00 +0000

The Binary System

All computer we act with on a daily base do not know about the decimal system we are using, based on the ten digits at our hands. All they know about are the states on and off. We build an imaginary circuit with a power source a control light - here an LED (Light Emitting Diode) - and a switch, closing the connection let the light flash. An off light counts as zero, and on light counts as one. Simple as it.We switch the light on and get a one.

04_Signs

Sun, 06 Feb 2022 00:00:00 +0000

Extending the binary system

While in the previous blog post about addition, the binary numbers had only one interpretation, we extend the system here to include negative (integer) numbers.

The simplest approach we can think of is to use the most significant bit (MSB) as sign bit, where '0' ist intepreted as sign '+' and '1' is interpreted as '-'. However, as we see in the following calculation this does not work as expected:

05_ALU

Fri, 11 Mar 2022 00:00:00 +0000

The ALU, the swiss knife of every cpu

Today the author wants to introduce an important part of every cpu: The arithmetic logic unit (ALU), we already know about some functions presented in the blog posts before. In this post we want to close the gaps systematically. Time for a short recap: The logic functions 'and','or','not' and 'xor' were introduced, also the arithmetic functions 'add' and 'sub' for integers were shown. Now we want to build most of those functionalities in one unit, the 1-bit alu cell.

06_priority_encoder_and_decoder

Tue, 23 Dec 2025 00:00:00 +0000

Hello Folks,

today we want to have a peek look into cascaded combinatorics with the example of priority encoder and decoders…. Second, we will introduce Karnaugh maps to do the optimization part.

Cascaded combinatorics and Priority encoder

First of all, what is a priority encoder? And for what is it used? This we can explain in a first simple list.

As interrupt controller to prioritise
As a code converter in a flash ADC.

07_Memory

Sun, 20 Mar 2022 00:00:00 +0000

Memory Organization

In this blog post the author will introduce the different types of semiconductor memory. This is a wide field, so the goal here is to focus on the most important ones and draw the differences between the different types.

The Memory hierarchy

As in computing all is about performance, we first have a look at the memory hierarchy. As you can see in the pyramid below, memory is ordered in layers. The slowest elements -also the ones with highest latency - are at the bottom of this pyramid, while the fastest ones are shown at the apex. Imagine your desk is the actual CPU, with an open book laying in front of your eyes. This is the register. Now you read in this book a reference to another book in your bookshelf. Your bookshelf is the cache here. The cache itself is again layered. Lets say L1-cache is the bookshelf in your room, L2-cache the bookshelf in another room and L3-cache books stored in a box in the same room. If you now have a reference in your current book (the one on your desk), that refers to a book you do not possess, you need to go to the public library. The public library is your RAM. The access times are really high. And lets say the book you need is also not available there, and they must order it from a library in another city. Then you got to the level at the bottom, which is the disk storage unit.

08_RISC-V

Mon, 21 Mar 2022 00:00:00 +0000

Digital design meets computer architecture

RISC vs CISC and The RISC-V architecture

Existing processor types can be classified by their instruction type set: Reduced instruction set computer (RISC), Complex instruction set computer (CISC) and hybrid forms. While mini processors like ARM for embedded systems mostly utilise reduced instruction sets,todays workstation and Server Architectures (x86, x86_64) are hybrids of RISC and CISC. The idea of a reduced instruction set is to avoid big complex instructions and multiple different addressing modes (as those typically used in x86 architectures). Advantages of a RISC architecture are shorter pipelines which allows faster clocking. RISC architectures follow a simple scheme: 'Fetch → Decode → Fetch Operands → Execute → Write Back' Also instructions have a constant length, memory operations are divided from arithmetic operations, which is known as Load/Store-architecture. RISC-V is an open standard for the instruction set archtitecture (ISA). Most of this post is referenced from the popular book Computer Organization and Design (RISC-V) Edition by Hennessey and Patterson.

11_sequential_logic

Mon, 01 May 2023 00:00:00 +0000

Sequential Logic

Complementary to Combinatorial logic, sequential logic contains some type of memory, making the behaviour state-dependent. We need to feed it a clock signal.

Mealy and Moore Automata (synchronous)

There are two different types of finite automata in the digital logic. Those are:

The mealy automata, which is dependent on the input and the state
The moore automata, which is only dependent on the state

12_Clocks_flipflops_and_registers

Sat, 12 Mar 2022 00:00:00 +0000

Clocks, Flipflops and registers

In this blog post the author will introduce multiple elements needed at a later stage.

Register-Transfer-Level needs a clock source

As for now we only learned about combinatiorial logic, which works without any clock source - every signal is just delayed by the time it needs to travel through the circuit. This is known as asynchronous. But for more sophisticated tasks, sequential circuits, having registers storing the input and output signals are necessary to get correct results. This is known as synchronous. Most, if not all designs used nowadays are synchronous, due to a lower design complexity.

Prequel: Introduction to electronics - 102

Wed, 21 Jun 2023 00:00:00 +0000

After this chapter you will know all the basics around time-sensitive components like coils and capacitors and simple circuits utilizing those components…

Electronics 102

Time-sensitive components

After reviewing and extensively describing the most important component, the resistor, in the first part, now we want to have a look at the next important component, the capacitor. Capacitor are also passive components, meaning they do not amplify a signal.

The transistor: Further Applications

Mon, 06 Apr 2026 00:00:00 +0000

After this chapter you will know all the basics around the semiconductor component transistor (BJT as well as MOSFETs) and their effects…

The transistor belongs an own chapter, thanks to its gamechanging influence to a complete new generation of electronics in the 1970ies to 1980…

The transistor is a nonlinear component , a device whose current–voltage relationship is not proportional. In other words, the current does not increase linearly with the applied voltage.

Introduction to electronics - 103 - nonlinear components

Tue, 07 Oct 2025 00:00:00 +0000

After this chapter you will know all the basics around semiconductor components like diodes, transistors (BJT as well as MOSFETs) and their effects…

A nonlinear component is a device whose current–voltage relationship is not proportional. In other words, the current does not increase linearly with the applied voltage.

Examples of nonlinear components include: * diodes (conduct current only in one direction), * transistors (whose behaviour depends on internal semiconductor junctions), * and CMOS structures.

Introduction to electronics - 104 - amplifier circuits

Tue, 07 Oct 2025 00:00:00 +0000

After this chapter you will know all the basics around linear components, integrated amplifiers and op-amps…

Integrated NF amplifiers

Today, much-needed electronic functions such as NF amplifiers are no longer predominantly constructed from “discrete” (from Latin discretum = separate) components, but are replaced by integrated circuits (Latin integrare = to unite); colloquially, they are called ICs (from English integrated circuit). Monolithic integrated circuits (from Greek monos = one, Greek lithos = stone, crystal) are particularly widespread. Here, a single silicon wafer measuring one or a few mm² in size is used to house a wealth of transistors, diodes, resistors, and capacitors of small capacity are accommodated on a single silicon wafer using planar technology, which together perform an overall function, e.g., that of a complete low-frequency amplifier, receiver, timer, computer, clock, etc. Only larger components such as capacitors of large capacity, coils, and, of course, the executive organs such as loudspeakers, digital displays, etc. are added discretely. Integrated circuits work extremely reliably because they allow electronic complexity to be achieved in a very small space, which would be difficult to finance with discrete components. In an IC, a transistor function costs a tenth of a cent. In consumer electronics, too, ICs are increasingly replacing discrete circuits. Integrated NF amplifiers usually consist essentially of an operational amplifier as a preamplifier and a push-pull output stage. A special feature of the operational amplifier is its input stage, which is designed as a differential amplifier. Therefore, we will first discuss the principle of the differential amplifier, followed by the basic characteristics of the operational amplifier, insofar as they are necessary for understanding the integrated low-frequency amplifier components.

Introduction to electronics - 105 - integrated circuits

Thu, 25 Sep 2025 00:00:00 +0000

This page is still under construction

Introduction to Analog-Digital-converters and Digital-Analog-Converters

Tue, 30 Dec 2025 00:00:00 +0000

The two important pillars - Digital-Analog-Converter and Analog-Digital-Converter

What we haven’t checked yet in our journey around (analog) electronics and digital electronics where the converter circuits from analog to digital and vice versa - for this we first want to explain the different terms around.

The theory about analog signals, digital signals, sampling and quantisation

Analog signals are characterized by being continuous in time and continuous in value. The conversion process of analog signals is often referred to as quantization.

Storytelling and the order of things

Sat, 12 Jul 2025 00:00:00 +0000

Storytelling and the order of things

Hey reader,

today I want to talk with you about the (right) order of things and its importance. When creating my first blog articles about electronics I hit multiple times the same obstacle, which is the order of things.

When trying to teach people about one of my favourite things I almost over the same amount of time, I am thinking about the educational purpose to the reader. That happened to me years ago, when I started this blog, and its happened to me ever since in a regular manner. So, for the existing blog posts, I came up with the following order (starting with linear components): (1) Resistors, then (2) capacitors and its counterpart coils, then - as last group, (3) - all the nonlinear components. Last but not least we want to discuss integrated circuits (IC) which are made of all components before - with exception to the coils which are hardly to made up in silicon. For the nonlinear components I will also try to get an educational purposeful order, so we want start here with the diode, then get to LEDs then to (MOSFET) transistors…

Oscillators - the hidden heart and engine behind all synths

Mon, 13 Apr 2026 00:00:00 +0000

The oscillator(s) - what it is and how it is working behind the scenes…

With exception to noise every synthesizer needs some swinging circuit - better known as an oscillator. There are pleanty of circuits doing that thing but we want to look first into Low-frequency oscillator, better known as LFO…

A simple (LF)O

Think of this circuit as a high-speed game of electronic tag between two sections of the op-amp. It’s a self-sustaining loop where each part is constantly reacting to the other to keep the signal moving.

Introduction to C++ (Qt GUI - Part I)

Tue, 10 Mar 2026 00:00:00 +0000

A GUI is a fantastic idea… But what should it be - SDL, wxWidgets, or Qt?

Choosing a GUI framework for a C++ audio project is a "fork in the road" moment. Each of these options pulls the project in a completely different architectural direction.

Since your course currently uses SDL, it’s the natural frontrunner, but here is how they stack up for a synth-building context:

Introduction into C++ (CMake interlude)

Thu, 05 Mar 2026 00:00:00 +0000

Introduction to efficient build tools for C++ projects

We now reach a rite of passage by moving from a Make-based build process to a CMake-based workflow.

The traditional "rule of three" (found in many classic open-source projects) — ./configure && make && sudo make install — is gradually being replaced by the CMake approach. This modern workflow typically involves creating a separate build directory to keep the source tree clean (so-called "out-of-source builds"):

Introduction into C++ (Part 6)

Sun, 01 Mar 2026 00:00:00 +0000

Introduction to the topics data structures, algorithms and complexity / computability in C++

Caution - this tutorial is a theory-loaded one - we will discuss a bit of the basics about data structures, algorithms and complexity - all that especially in context with C - so let's get started with the data structures in C

Lists, Dictionaries and Queues

We begin with some basic data structures we already used without going much into the topics; those two are std::vector (basically lists) and std::map (basically dicts).

Introduction into C++ (Part 5)

Sat, 07 Feb 2026 00:00:00 +0000

Beyond the Single Note: Implementing Polyphony

In our previous tutorials, our synthesizer was limited to one note at a time. If you pressed a new key, the old sound simply disappeared. Today, we change that by implementing Polyphony—the ability to play chords and manage multiple "Voices" simultaneously.

1. What is a "Voice"?

In professional synthesizer design, we use the Voice Architecture. A "Voice" is a self-contained unit that holds everything needed to produce one sound: an Oscillator and an Envelope.

Introduction into C++ (Part 4)

Thu, 05 Feb 2026 00:00:00 +0000

From Stateless to Stateful: Filters & Composition

In previous parts, we built an oscillator. It was "stateless"—you give it a phase, it gives you a value. It doesn’t care what happened a microsecond ago. But to make music sound "warm" or "organic," we need objects that have a memory.

1. DSP General: The Concept of State

In Digital Signal Processing (DSP), a filter is stateful. To calculate the current output, a filter needs to know the previous output.

Introduction Course to C++

Sun, 01 Feb 2026 00:00:00 +0000

This course introduces C++ programming through the development of a small audio / synthesizer application.

The goal is to learn the language step-by-step while building a working audio system.

Prerequisites:

A Linux system (Debian or Ubuntu recommended)
GCC (GNU Compiler Collection)
The make build tool
Basic familiarity with the command line
Some mathematical background (helpful for the audio and signal-processing sections)

Windows users can follow the course using Windows Subsystem for Linux (WSL).

Introduction to electronics Course

Sun, 01 Feb 2026 00:00:00 +0000

Electronics 101–104 — Overview

This page provides a short overview of the electronics introduction series.

Electronics 101

electronics 101

Introduction to basic electrical concepts such as current, voltage, resistance, and simple circuits.

Electronics 102

electronics 102

Covers time-dependent components like capacitors and coils, also simple passive filters.

Electronics 103

electronics 103

Introduces nonlinear components including diodes, transistors, and their use as switches and amplifiers.

Electronics 104

electronics 104

Introduction into C++ (Part 3)

Thu, 29 Jan 2026 00:00:00 +0000

Introduction into C++ (Part 3)

C++ OOP Mastery: The Power of Composition (Has-A)

In software architecture, there are two primary ways to connect objects: Inheritance (Is-A) and Composition (Has-A). While beginners often try to solve everything through inheritance ("An Oscillator is an Envelope"), professionals prefer composition: "A Synthesizer has an Envelope."

1. Why Composition?

Think of our synthesizer as a modular rack. Each module (Oscillator, Envelope) is an independent class. The SynthEngine acts as the chassis where these modules are plugged in.

Introduction into C++ (Part 2)

Wed, 21 Jan 2026 00:00:00 +0000

Introduction into C++ (Part 2)

In this next example / tutorial we will have a look at sound producing program (aka a synth), for which we utilize the SDL library (Simple direct media library). We will go about the program, line for line and explain the different items.

Lets begin…

First of all we have the includes for the SDL library, we will have a look at the header file later. Also we include cmath for math and iostream for in- and output (but in this example only output).

Introduction into C++

Tue, 20 Jan 2026 00:00:00 +0000

A simple introduction into C++

Hello folks, this time I want to start with a series about programming with C++. While Python is a general purpose programming language, C++ is often chosen when you need tighter control over performance and latency.

We start simple by creating a short program that spits out the limits for the different data types. Install Microsoft code so that have one simple IDE you can work with…

A short guide to Interrupts

Sat, 03 Jan 2026 00:00:00 +0000

Interrupts - The doorbell analogy

Imagine a person sitting quietly at home, deeply focused on reading a book. This person represents the CPU, and the act of reading represents the normal execution of a program. In a world without doorbells, the only way to know whether someone is at the door would be to repeatedly stop reading, walk over, and check the door. Most of the time this effort would be wasted, because nobody is there.

00_combinatorial_logic

Sat, 16 Apr 2022 00:00:00 +0000

This course about digital logic is splitted into two big chunks:

Combinatorial circuits (without memory elements)
Sequential circuits (with memory elements)

While combinatorial circuits consists of boolean gates interconnected without feedback function, sequential gates posses a memory function,which makes them able to progress to another state.

A combinatorial circuit can have n -wide vector of inputs and an m -wide vector of outputs.

Prequel: Introduction to electronics

Sat, 23 Jan 2021 00:00:00 +0000

After this chapter you will know all the basics around electricity and simple circuits utilizing ohmic load…

Prequel Introduction to electronics

While I was about to write the implementation part of the boolean algebra post, the basic logic gates, the writing process got quickly out of hand and I caught myself to write more about less connected topics like explaining basic electronic components and their implementation on silicon than the actual content, here shall be the place for those excursions. This is not meant to be a complete reference more a supplement to existing literature. '''

Bits & pieces - Sven Wehrend

01_boolean_algebra

Boolean Algebra and Basic Logic Gates

How does a CPU work? Overview

Introduction and Overview

How does a CPU work 2? Overview

How does a CPU work 2 - Table of contents

From Combinatorial to Sequential Logic - Introduction

Clocks,Flipflops and registers

02_XOR

03_binary_system

The Binary System

04_Signs

Extending the binary system

05_ALU

The ALU, the swiss knife of every cpu

06_priority_encoder_and_decoder

Cascaded combinatorics and Priority encoder

07_Memory

Memory Organization

The Memory hierarchy

08_RISC-V

Digital design meets computer architecture

RISC vs CISC and The RISC-V architecture

11_sequential_logic

Sequential Logic

Mealy and Moore Automata (synchronous)

12_Clocks_flipflops_and_registers

Clocks, Flipflops and registers

Register-Transfer-Level needs a clock source

Prequel: Introduction to electronics - 102

Electronics 102

Time-sensitive components

The transistor: Further Applications

Introduction to electronics - 103 - nonlinear components

Introduction to electronics - 104 - amplifier circuits

Integrated NF amplifiers

Introduction to electronics - 105 - integrated circuits

Introduction to Analog-Digital-converters and Digital-Analog-Converters

The two important pillars - Digital-Analog-Converter and Analog-Digital-Converter

The theory about analog signals, digital signals, sampling and quantisation

Storytelling and the order of things

Storytelling and the order of things

Oscillators - the hidden heart and engine behind all synths

The oscillator(s) - what it is and how it is working behind the scenes…​

A simple (LF)O

Introduction to C++ (Qt GUI - Part I)

A GUI is a fantastic idea…​ But what should it be - SDL, wxWidgets, or Qt?

Introduction into C++ (CMake interlude)

Introduction to efficient build tools for C++ projects

Introduction into C++ (Part 6)

Introduction to the topics data structures, algorithms and complexity / computability in C++

Lists, Dictionaries and Queues

Introduction into C++ (Part 5)

Beyond the Single Note: Implementing Polyphony

1. What is a "Voice"?

Introduction into C++ (Part 4)

From Stateless to Stateful: Filters & Composition

1. DSP General: The Concept of State

Introduction Course to C++

Introduction to electronics Course

Electronics 101–104 — Overview

Electronics 101

Electronics 102

Electronics 103

Electronics 104

Introduction into C++ (Part 3)

Introduction into C++ (Part 3)

C++ OOP Mastery: The Power of Composition (Has-A)

1. Why Composition?

Introduction into C++ (Part 2)

Introduction into C++ (Part 2)

Introduction into C++

A simple introduction into C++

A short guide to Interrupts

Interrupts - The doorbell analogy

00_combinatorial_logic

Prequel: Introduction to electronics

Prequel Introduction to electronics

The oscillator(s) - what it is and how it is working behind the scenes…

A GUI is a fantastic idea… But what should it be - SDL, wxWidgets, or Qt?