Code - The Hidden Language of Computer Hardware and Software

This is the sixth installment in a series of posts where I share notes taken while reading an interesting book or article.

This post includes the notes made while reading the book “Code - The Hidden Language of Computer Hardware and Software 2nd Edition” by Charles Petzgold.

Chapter 2: Codes and Combinations

• Morse Code is a binary language. International Morse Code encodes up to 8 bits of information where each bit is either a dot or a dash.
• Dots and dashes are the written representation of Morse Code. The dot is a short signal, while the dash is a long signal. The length of the dash is three times that of the dot.
• As with all binary codes, each time you add a bit, you double the number of possible combinations.

Chapter 3: Braille and Binary Codes

• Braille is a type of binary code where 6 bits represent a character. The 6 bits arrange in a 3x2 grid, where each dot can be either raised or not raised. The 6 bits can represent 64 different characters.
• Though there are only 64 characters, Braille characters can have additional meanings based on their context.
• The number indicator marks the beginning of a sequence of numbers. The letter indicator terminates the number sequence. This is an example of a shift code.
• In Braille, the capital indicator capitalizes the letter that follows. The capital indicator is an example of an escape code. Escape codes change the meaning of the code that immediately follows.

Chapter 4: Anatomy of a Flashlight

• You can characterize electricity as the flow of electrons.
• In the flashlight example, the battery is the source of electricity. The flashlight bulb is the load. The switch is a control device that opens and closes the circuit.
• Batteries produce a chemical reaction that creates a flow of electrons. Chemical energy converts to electrical energy. Spare electrons appear on the anode side of the battery. The cathode side of the battery has a deficiency of electrons. Electrons would like to flow from the anode to the cathode.
• An electrical circuit provides a path for the flow of electrons from the anode to the cathode.
• Substances composed of atoms that bias towards shedding electrons are conductors. Copper, silver, and gold are good conductors.
• The opposite of conductance is resistance. Substances with high resistance are called insulators. Rubber, glass, and plastic are good insulators.
• Current (\(I\)) is the flow of electrons through a circuit.
• Voltage (\(V\)) is the difference in electric potential between two points in a circuit.
• Voltage is directly proportional to the amount of current flowing through a circuit. Current is inversely proportional to resistance. Also known as Ohm’s Law: \(V = IR\).
• Power in Watts is the product of voltage and current: \(P = IV\).

Chapter 5: Communicating Around Corners

• You can make a primitive telegraph by connecting two batteries, four wires, and two light bulbs.
• You can remove a wire from the circuit by using a common ground. Ground in this case means a connection to the Earth.
• The Earth acts a source of electrons. The electrons flow from the Earth, through the circuit, and into the positive terminal of the battery.
• American Wire Gauge (AWG) is a measure of wire thickness. The lower the number, the thicker the wire. The thicker the wire, the less resistance it has.
• When covering great distances, you need to use thicker wire or a higher voltage power supply.

Chapter 6: Logic with Switches

• George Boole invented Boolean algebra. Boolean algebra is a system of logic.
• You can describe boolean algebra in terms of sets. The usual set operators such as union, intersection, and complement apply as do the concepts of the universe and NULL set.
• Two switches wired in series are equivalent to an AND gate.
• Two switches wired in parallel are equivalent to an OR gate.
• You can configure switches and wires to form complex boolean expressions. A primitive form of a computer.

Chapter 7: Telegraphs and Relays

• The invention of the telegraph marks the beginning of modern communication. For the first time, people could communicate over long distances almost instantaneously.
• The telegraph key is a switch that opens and closes the circuit to send messages. The telegraph operator taps the key to send dots and dashes.
• The telegraph sounder is a device that converts the electrical signals from the telegraph key into audible sounds.
• One major impediment to the telegraph was the length of the wires needed to connect the telegraph stations. The longer the wire, the more resistance it has, and the weaker the signal.
• The invention of the relay solved the problem of long-distance telegraphy. A relay is an electrically operated switch that can amplify the signal.
• A relay consists of an electromagnet, a set of contacts, and a spring. When the electromagnet gets energized, it attracts the armature, which closes the contacts and completes the circuit.

Chapter 8: Relays and Gates

• Reduced to its essentials, a computer is a synthesis of Boolean algebra and electricity.
• The crucial components of a computer are the logic gates. Logic gates are electronic circuits that perform boolean operations.
• Like switches, you can connect relays in series or parallel as logic gates. You can combine logic gates to form more complex circuits.
• The switches control the input to the relays, and the relays control the output. The output of one relay can be the input to another relay.
• A normally open relay is a relay that’s open when the electromagnet isn’t energized. A normally closed relay is a relay that’s closed when the electromagnet isn’t energized.
• An inverter is a logic gate that reverses the input signal. In terms of relays, an inverter is a normally closed relay that opens when the electromagnet gets energized.
• There are six basic logic gates: AND, OR, NOT, NAND, NOR, and XOR.
• Additionally, you have buffers. A buffer is a logic gate that passes the input signal to the output without changing it. In real life circuits, sometimes output must serve as many inputs. That’s called fanout, and it can result in a lessening of the power available to each input. Buffers can help boost that power acting as a relay. You can also use buffers to delay a signal.
• From a NAND or NOR gate, you can create all other logic gates.
• The following are Demorgan’s Laws:
  • \(\lnot A \land \lnot B = \lnot(A \lor B)\)
  • \(\lnot A \lor \lnot B = \lnot(A \land B)\)
• Demorgan’s Laws are useful for simplifying boolean expressions.

Chapter 9: Our Ten Digits

• There are many possible number systems.
• Roman numerals were common before the introduction of the Hindu-Arabic numeral system. Key features that differentiate the Hindu-Arabic numeral system include:
  • The use of a zero to represent the absence of a value.
  • The positional notation, where the value of a digit depends on its position in the number.

Chapter 10: Alternative 10s

• By convention, humans work in a base 10 number system, also known as decimal.
• There are many other number systems, such as binary (base 2), octal (base 8), and hexadecimal (base 16).
• The formula for converting from any base to decimal is: \(d = \sum_{i=0}^{n} d_i \cdot b^i\) where \(d\) is the decimal value, \(d_i\) is the digit in base \(b\), and \(n\) is the position of the digit.
• Binary numbers unite arithmetic and electricity. Switches, wires, and light bulbs can all represent the binary digits 0 and 1, and with the addition of logic gates, you can manipulate these numbers.

Chapter 11: Bit by Bit by Bit

• The binary number system is the simplest number system possible.
• The bit, a binary digit, is the fundamental unit of information in computing.
• The meaning of a particular bit or collection of bits is always understood contextually.
• You can visualize binary codes in many ways. The example given is the Universal Product Code (UPC) barcode. The UPC barcode is a binary code that encodes information about a product. A slice of the barcode has black lines representing 1 and gaps representing 0. The thickness of the lines or gaps dictate the number of bits represented (up to 4 bits per line). In total, the UPC barcode encodes 95 bits of data.
• The UPC barcode also includes some error checking. The last digit is a checksum that verifies the integrity of the data. Each barcode includes a beginning, middle, and end guard pattern to help scanners identify faulty codes.
• Quick Response (QR) codes are another example of a binary code. QR codes can encode more information than UPC barcodes, including URLs and text. QR codes consist of black squares arranged on a white grid. The black squares represent 1s, and the white squares represent 0s. Most of the bits in a QR code are for error correction.

Chapter 12: Bytes and Hexadecimal

• Computers often group bits into a quantity called a word with the most common word size being 8 bits, also known as a byte.
• Modern computers typically use 32-bit or 64-bit words.
• The hexadecimal number system is a base 16 number system that uses the digits 0-9 and the letters A-F to represent values.
• You can group the digits in a binary number into sets of four to form a hexadecimal digit.

Chapter 13: From ASCII to Unicode

• Morse code is a variable bit-length code, meaning that different characters can have different numbers of bits. For example, the letter ‘E’ is a single dot (1 bit), while ‘Q’ is a dash followed by two dots (3 bits).
• Braille is a fixed-length code, meaning that each character has the same number of bits (6 bits).
• ASCII (American Standard Code for Information Interchange) is a character encoding standard that uses 7 bits to represent characters. ASCII can represent 128 different characters, including letters, digits, and control characters.
• ASCII includes 32 control characters that are not printable, such as the newline character and the tab character.
• ASCII is also known as plain text. ASCII data does not include any formatting information, such as font size or color.
• Extended ASCII is an 8-bit character encoding that includes additional characters beyond the standard ASCII set. Extended ASCII can represent 256 different characters.
• Extended ASCII can’t represent characters from all different languages and scripts.
• Unicode is a character encoding standard that can represent characters from many different languages and scripts. Unicode started as a 16-bit encoding.
• Unicode documents start with a Byte Order Mark to indicate endianness.
• Unicode has more recently extended to 21 bits, allowing it to represent over a million different characters.
• Unicode transformation formats (UTF) encode Unicode characters in a way that’s compatible with existing systems. The most common UTFs are UTF-8, UTF-16, and UTF-32.
• UTF-8 is the most widely used Unicode encoding. It uses 1 to 4 bytes to represent characters, depending on the character’s code point. How bytes are interpreted is complex enough that you should look this up for more details.

Chapter 14: Adding with Logic Gates

• The summation of two bits produces a sum bit and a carry bit.
• You create an XOR gate by passing the two inputs through both a OR gate and a NAND gate, and then passing the outputs through a AND gate:
• An XOR gate takes two input bits and produces a sum bit.
• An AND gate takes two input bits and produces a carry bit.
• You can combine XOR and AND gates to create a half adder, which adds two bits and produces a sum bit and a carry bit.
• A full adder is a circuit that adds three bits: two input bits and a carry bit from a previous addition. A full adder produces a sum bit and a carry bit. You can combine two half adders and an OR gate to create a full adder (see page 177).
• You can combine two 8 bit full adders to create a 16 bit adder (see page 182). You can combine multiple 16 bit adders to create larger adders.

Chapter 15: Is This For Real

• Relays and vacuum tubes were the first electronic components used in computers.
• You can build logic gates from vacuum tubes just like you can with relays.
• Relays suffer slow switching speeds and are susceptible to mechanical wear.
• Vacuum tubes are faster than relays but are larger, consume more power, generate more heat, and wear more often.
• The transition from relay technology to vacuum tube technology marked the transition from electromechanical computers to electronic computers.
• Von Neumann architecture is a design for a computer that uses a single memory space for both data and instructions. This architecture is the basis for most modern computers.
• You can control a semiconductors’ conductance by applying a voltage. This property makes them ideal for building logic gates and other electronic components.
• Semiconductor doping is the process of adding impurities to a semiconductor to change its electrical properties. The most common dopants are phosphorus and boron forming n-type and p-type semiconductors.
• You can make amplifiers out of semiconductors by sandwiching a p-type semiconductor between two n-type semiconductors. This is the basis for a NPN transistor, and the three pieces form the collector, base, and emitter.
• A small voltage on the base controls the flow of current between the collector and emitter.
• The transistor introduces solid-state electronics, which means transistors are built from solids, specifically semiconductors and most commonly silicon.
• Transistors require much less power, generate much less heat, and last longer than vacuum tubes.
• The invention of the integrated circuit (IC) allowed for the miniaturization of electronic components. An IC is a small chip that contains many transistors and other electronic components.
• The first ICs were usually packaged in dual in-line packages (DIPs).
• There are two families of ICs: transistor-transistor logic (TTL) and complementary metal-oxide-semiconductor (CMOS).
• TTL chips are faster but consume more power than CMOS chips. CMOS chips are slower but consume less power and are more tolerant to variations in voltages.
• One important fact to know about a particular integrated circuit is the propagation time, the time it takes for a change in the inputs to reflect in the output.
• You measure propagation time in nanoseconds.
• The timeline to keep in mind from this chapter is that logic gate components trended from relays, to vacuum tubes, to transistors, and then to integrated circuits.

Chapter 16: But What About Subtraction

• This chapter introduces two’s complement, a method for representing signed integers in binary.
• Two’s complement makes for easy addition and subtraction of signed integers using the same binary addition circuits previously discussed.
• To convert a positive integer to two’s complement, you simply represent it in binary. To convert a negative integer to two’s complement, you invert the bits of its positive representation and add 1.
• Since binary numbers have a fixed number of bits, you can only represent integers within a certain range. For example, with 8 bits, you can represent signed integers from -128 to 127 or unsigned integers from 0 to 255.
• There’s opportunity for overflow when adding or subtracting signed integers. The circuit on page 210 shows how to detect overflow in a two’s complement addition circuit.

Chapter 17: Feedback and Flip-Flops

• You can create an oscillator by connecting the output of an inverter to its input. The inverter will toggle its output between 0 and 1, creating a square wave.
• The period of an oscillator is the time it takes for the output to complete one cycle. The frequency is the number of cycles per second.
• The frequency of an oscillator is inversely proportional to its period. Usually, you measure frequency in Hertz.
• See page 221 for an illustration of a reset-set flip-flop.
• The next flip-flop type is the level triggered D-type flip-flop. The D stands for data. The D flip-flop captures the value of the data input when the clock signal is high and holds that value until the next clock cycle.
• A edge triggered D-type flip-flop captures the value of the data input on the rising or falling edge of the clock signal.
• You can make an edge triggered D-type flip-flop by combining two level triggered flip-flops (see page 229).
• If you combine an oscillator with a edge triggered D-type flip-flop, you can create a frequency divider. The output frequency is half the input frequency. See page 235 for an illustration of a frequency divider.
• Chained frequency dividers create a binary counter called a ripple counter.
• To find the frequency of the oscillator, you can let the ripple counter run for a certain number of cycles and then divide the number of cycles by the time it took to run them.
• You can augment a flip-flop with a clear and preset input. You never set both clear and preset at the same time.
• Having a clear input avoids the issue of the flip-flop being in an indeterminate state when powered on.
• With the preset input, you can set the flip-flop to a known state without waiting for the clock signal.

Chapter 18: Let’s Build a Clock

• Binary Coded Decimal (BCD) is a way of representing decimal numbers in binary. BCD uses 4 bits to represent each decimal digit, allowing you to represent decimal numbers from 0 to 9.
• It’s best to read the book to get an idea of how to build the clock. At a high level, you use a ripple counter to count each digit in the seconds, minutes, and hours. The output of the high digit’s counter is the input to the next counter. Additional circuitry makes it possible to display the hours in 12-hour format.
• Electrical current can only flow in one direction through a diode.
• A Light Emitting Diode (LED) is a diode that emits light when current flows through it.
• A diode matrix is a grid of diodes that displays characters or numbers. The diodes are in rows and columns, and you can turn on specific diodes to create a pattern.
• Diode matrices are technically a form of Read Only Memory (ROM).

Chapter 19: An Assemblage of Memory

• You can use level triggered D-type flip-flops to create a primitive form of memory.
• Combining say 8 flip-flops with a 3-to-8 decoder creates a memory cell that can store 8 bits of data. Add a 8-to-1 selector to the circuit and you’re able to read the data from the memory cell. See page 273 for an illustration.
• This is a form of read/write memory. Since you can address any of the 8 bits at will, this is also known as Random Access Memory (RAM).
• A tri-state buffer can have one of three states: high, low, or high impedance (Z). The high impedance state is like an open circuit, meaning it doesn’t affect the output.
• Both static and dynamic RAM are examples of volatile memory, meaning they lose their contents when powered off.

Chapter 20: Automating Arithmetic

• You can build a simple adder using components introduced in previous chapters. This includes RAM, accumulators, and latches.
• The control signals are the most complex part of the adder.
• The adder includes simple instructions or opcodes for adding and subtracting, storing results in RAM, and halting the machine.
• The combination of the hardware and software forms a primitive computer.
• Byte ordering specifically little versus big endian is important when dealing with multi-byte data types.

Chapter 21: The Arithmetic Logic Unit

• The three components of a computer include memory, the central processing unit (CPU), and input/output (I/O) devices.
• In memory lives both the data and the CPU instruction codes.
• The Arithmetic Logic Unit (ALU) is the part of the CPU that performs arithmetic and logic operations.
• The ALU shown in this chapter can add and subtract 8-bit numbers and perform bitwise logic operations on the same 8-bit numbers.
• There are opcodes for each ALU function.
• The ALU performs all logic operations simultaneously outputting each result to a tri-state buffer. Three functions bits select which buffer to output.
• A compare operation is the same as a subtraction operation, but the result is not stored. Instead, you save a carry flag and a zero flag.
• You can find the complete ALU circuit on page 332.

Chapter 22: Registers and Busses

• A CPU includes a small number of special purpose registers.
• The registers can be general purpose or serve a specific task. For example, in the Intel 8080 CPU, the accumulator register is a general purpose register used to store intermediate results of arithmetic and logic operations.
• The opcodes may use one or more registers as operands. For example, the Intel 8080 CPU has an opcode for moving data to RAM. The opcode uses the H and L registers to form the 16-bit address of the RAM location to write to.
• Assembly language is a low-level programming language that uses mnemonics to represent opcodes and registers. Each assembly language instruction corresponds to a single opcode.
• Opcodes for arithmetic, moving data to registers/ram, control flow, and halting the CPU exist.
• The data bus is a set of wires that carry data between the CPU, memory, and I/O devices. The address bus is a set of wires that carry addresses to memory and I/O devices.

Chapter 23: CPU Control Signals

• Most control signals are of two types (buses here are the data and address busses):
  • Signals that put a value on one of the two busses.
  • Signals that save a value from one of the two busses.
• Signals that put a value on the bus attach to the enable inputs of various tri-state buffers that connect the outputs of the components to the bus.
• Signals that save a value from the bus usually control the clock inputs of the various latches that connect the busses to the components on the bus. The only exception is when you save a value to memory using the RAM write signal.
• CPU cycles are the time it takes to execute a single instruction. When optimizing for speed, you want to minimize the number of CPU cycles needed to execute a program.
• The control signals are arguably the most complex part of the CPU.

Chapter 24: Loops, Jumps, and Calls

• Loops are a fundamental control flow construct in programming. Loops repeat a block of code multiple times.
• To implement a loop in assembly language, you need to use a combination of jump instructions and conditional flags.
• Subroutines or functions are groups of instructions.
• The CALL and RET instructions call and return from subroutines.
• The stack is a special area of memory used to store temporary data. The stack provides a means to save the state of the program when calling a subroutine and to restore it when returning from the subroutine.
• You can nest subroutine calls, meaning you can call a subroutine from within another subroutine. It’s possible to nest so many calls that you run out of stack space resulting in a stack overflow. You can also underflow the stack by popping more items than you pushed onto it.

Chapter 25: Peripherals

• Devices such as the mouse, keyboard, video display, and printer fall under the category of peripherals.
• One of the most important peripherals is the video display. The video display renders pixels on the screen. Each pixel is a small dot of color. Each pixel is a combination of 8 bit red, green, and blue (RGB) values. A display with a 1920x1080 resolution has 2,073,600 pixels, each represented by 3 bytes requiring a total of 6MB of memory to store the pixel data.
• The frame buffer is an area in main memory that houses the display pixels. The frame buffer is an example of a memory-mapped I/O device. The CPU can read and write to the frame buffer as if it were regular memory.
• Peripherals often communicate with the CPU using interrupts. An interrupt is a signal that tells the CPU to stop what it’s doing and handle a specific event.
• Many signals are analog. To convert an analog signal to a digital signal, you need an Analog-to-Digital Converter (ADC). An ADC samples the analog signal at regular intervals and converts each sample to a digital value. Digital-to-Analog Converters (DAC) do the opposite, converting digital values to analog signals.
• DACs in video displays convert the digital values of the pixels into voltages that govern the intensity of the red, green, and blue components of each pixel.
• Digital cameras use ADCs to convert the analog signals from the camera sensor into digital values that form a bitmap.
• With image data such as a bitmap, you can use compression algorithms to reduce the size of the image. Common image formats include JPEG, PNG, and GIF. Some compression algorithms are lossy, meaning they discard some data to reduce the file size, while others are lossless, meaning they preserve all the original data. JPEG is lossy while PNG and GIF are lossless.
• Microphones take in sound waves and convert them into electrical signals. The electrical signals are analog, so you need an ADC to convert them into digital values.
• Compact discs (CDs) store audio data in a digital format. Pulse Code Modulation (PCM) is the technique which encodes the data. PCM samples the audio signal at regular intervals and quantizes the amplitude of the signal to a fixed number of levels.
• You sample audio at a rate of 44.1 kHz, meaning you take 44,100 samples per second. Each sample is typically 16 bits, resulting in a data rate of 1,411.2 kbps for stereo audio (two channels). The Nyquist Theorem states that you need to sample at least twice the maximum frequency to accurately capture the audio signal.
• Much like pictures, you can also compress audio data. Common audio formats include MP3, AAC, and FLAC. MP3 and AAC are lossy formats, while FLAC is a lossless format.

Chapter 26: The Operating System

• An operating system (OS) is a collection of software that manages computer hardware and software resources and provides common services for computer programs.
• An OS exposes an Application Programming Interface (API) that programs interact with to access hardware resources.
• The OS includes a filesystem that organizes files and directories on storage devices. The filesystem provides a way to read, write, and manage files.
• A bootloader is a small program that runs when the computer starts up. The bootloader loads the OS into memory and transfers control to it.
• In the early days, programmers would often bypass the OS and control the hardware directly usually via writing directly to memory.
• The introduction of operating systems that included a graphical user interface (GUI) made it easier for users to interact with the computer.

Chapter 27: Coding

• Assembly language is a low-level programming language that uses mnemonics to represent machine code instructions. Each assembly language instruction corresponds to a single machine code instruction.
• Assembly language is specific to a particular CPU architecture. For example, the Intel 8080 assembly language is different from the Motorola 6800 assembly language. In essence, assembly code is non-portable.
• A program called an Assembler translates assembly language code into machine code.
• High-level programming languages such as C, Python, and Java provide a more abstract way to write programs. High-level languages are more portable across different CPU architectures.
• A compiler translates high-level language code into machine code. The compiler performs various optimizations to improve the performance of the generated machine code.
• A functional programming language is a type of high-level language that treats computation as the evaluation of mathematical functions. Examples include Haskell and Lisp.
• A procedural programming language is a type of high-level language that uses procedures or routines to structure the code. Examples include C and Pascal.
• An object-oriented programming language is a type of high-level language that uses objects to structure the code. Examples include Java, C++, and Python.
• An interpreted language is a type of high-level language that a program called an interpreter executes one line at runtime. Examples include Python and Ruby. The interpreter reads the source code and executes it line by line.
• Most languages represent floating point numbers using the IEEE 754 standard. The standard defines how to represent floating point numbers in binary, including the sign bit, exponent, and mantissa.
• Special hardware called a floating point unit (FPU) performs arithmetic operations on floating point numbers. The FPU is often integrated into the CPU.

Chapter 28: The World Brain

• The Internet is a global network of interconnected computers that communicate with each other using standardized protocols.
• TCP/IP (Transmission Control Protocol/Internet Protocol) is the fundamental protocol suite that underlies the Internet.
• The World Wide Web (WWW) is a system of interlinked hypertext documents accessed via the Internet. The WWW uses the HTTP (Hypertext Transfer Protocol) to transfer documents.
• The Internet is a decentralized network, meaning there is no single point of control. This decentralization makes the Internet resilient to failures.
• Modems and routers are devices that connect computers to the Internet. A modem converts digital signals from a computer into analog signals sent over telephone lines or cable systems. A router directs data packets between different networks.
• The Domain Name System (DNS) is a distributed naming system that translates human-readable domain names (like www.example.com) into IP addresses.