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April 27 - July 21, 2022
The further back in time you go, the simpler the technologies become.
Although Morse code has absolutely nothing to do with computers, becoming familiar with the nature of codes is an essential preliminary to achieving a deep understanding of the hidden languages and inner structures of computer hardware and software.
code usually means a system for transferring information among people and machines.
A code is useful if it serves a purpose that no other code can.
The key word here is two. Two types of blinks, two vowel sounds, two different anything, really, can with suitable combinations convey all types of information.
Morse code is said to be a binary (literally meaning two by two) code because the components of the code consist of only two things—a dot and a dash.
electron theory, which says that electricity derives from the movement of electrons.
Lightning is a lot of electrons moving very quickly from one spot to another.
The thicker a wire, the lower the resistance it has. This may be somewhat counterintuitive. You might imagine that a thick wire requires much more electricity to “fill it up.” But actually the thickness of the wire makes available many more electrons to move through the wire.
Voltage refers to a potential for doing work. Voltage exists whether or not something is hooked up to a battery. Consider a brick.
Current is related to the number of electrons actually zipping around the circuit. Current is measured in amperes, named after André Marie Ampère (1775–1836), but everybody calls them amps, as in “a 10-amp fuse.” To get one amp of current, you need 6,240,000,000,000,000,000 electrons flowing past a particular point per second.
Current is similar to the amount of water flowing through a pipe. Voltage is similar to the water pressure. Resistance is similar to the width of a pipe—the smaller the pipe, the larger the resistance.
amount of water flowing through a pipe (the current) is directly proportional to the water pressure (the voltage) and inversely proportional to the skinniness of the pipe (the resistance).
The earth is to electrons as an ocean is to drops of water. The earth is a virtually limitless source of electrons and also a giant sink for electrons.
repeater, or a relay. A relay is like a sounder in that an incoming current is used to power an electromagnet that pulls down a metal lever. The lever, however, is used as part of a switch connecting a battery to an outgoing wire. In this way, a weak incoming current is “amplified” to make a stronger outgoing current.
Yes, the zero. The lowly zero is without a doubt one of the most important inventions in the history of numbers and mathematics.
What’s special about binary is that it’s the simplest number system possible.
In the computer age, the bit has come to be regarded as the basic building block of information.
information represents a choice among two or more possibilities.
any information that can be reduced to a choice among two or more possibilities can be expressed using bits.
The only requirement is that everyone who uses the code must know what the 0 and 1 bits mean.
in binary the number of possible codes is always equal to 2 to the power of the number of bits:
But most fundamentally, bits are numbers. All that needs to be done when bits represent other information is to count the number of possibilities. This determines the number of bits that are needed so that each possibility can be assigned a number.
Organon
logic was a means of analyzing language in the search for truth and thus was considered a form of philosophy.
The Mathematical Analysis of Logic, Being an Essay Towards a Calculus of Deductive Reasoning (1847)
An Investigation of the Laws of Thought on Which Are Founded the Mathematical Theories of Logic and Probabilities (1854), more conveniently referred to as The Laws of Thought.
In conventional algebra, the operands (which are usually letters) stand for numbers, and the operators (most often + and x) indicate how these numbers are to be combined.
Boolean algebra (as Boole’s algebra was eventually called), the operands refer not to numbers but instead to classes. A class is simply a group of things, what in later times came to be known as a set.
The + symbol in Boolean algebra means a union of two classes. A union of two classes is everything in the first class combined with everything in the second class. For example, B + W represents the class of all cats that are either black or white. The x symbol in Boolean algebra means an intersection of two classes. An intersection of two classes is everything that is in both the first class and the second class.
we can write F x T as F·T or simply FT (which is what Boole preferred).
The symbol 1 in Boolean algebra means “the universe”—that is, everything we’re talking about.
The other symbol that we need is the 0, and in Boolean algebra the 0 means an empty class—a class of nothing.
Law of Contradiction and indicates that something can’t be both itself and the opposite of itself.
When you form a union of two classes, you’re actually accepting things from the first class OR the second class. And when you form an intersection, you’re accepting only those things in both the first class AND the second class.
The + (previously known as a union) now means OR. The x (previously known as an intersection) now means AND. The 1 – (previously the universe without something) now means NOT.
Boolean test.
The output of one gate (or inverter) can be the input to one or more other gates (or inverters). But the outputs of two or more gates (or inverters) are never connected to one another.
The NAND gate
An AND gate with two inverted inputs does exactly the same thing as a NOR gate:
Formal Logic
The Mathematical Analysis of Logic.
When you come right down to it, addition is just about the only thing that computers do.
