Mathematical sciences {computer science, mathematics} can be about hardware and software.
computers
Computers input data; run application programs to perform arithmetic, logical, or string operations on input and intermediate data; and output data. Computers are information processors, general symbol manipulators, and efficient universal Turing machines.
Digital computers [Neumann, 1946] use off-on (binary code) switches, in switching networks of digital electronic circuits, to represent data and instructions. Electronic switching devices keep their current state until the next machine step resets switches. [Telephone exchanges are also switching networks, using switches with more than two positions (n-ary code).]
Analog computers use continuous voltage or current magnitudes in electronic circuits to represent numbers, calculate integrals, find slope or gradient, sense coincidences and anti-coincidences, time pulses, shape pulses, combine pulses, amplify pulses, invert pulses, and invert and amplify pulses.
computer parts
The central processing unit (CPU) runs the clock, reads input data from memory, reads program instructions, executes instructions, and writes output data to memories, screens, or printers.
The computer clock sends electric pulses at beginnings of CPU cycles (steps).
Computer memory stores data and instructions.
Input-output devices include tapes, disks, solid-state memories, printers, and screens.
CPUs and memories have registers for holding input values, output values, instructions, results, and register addresses. Information moves in sequence from one register to another, along one serial path or simultaneously on parallel paths.
operating system
Computer operating systems store system configuration, handle input-output operations, manipulate and process files, manage and allocate memory, and begin and end application programs.
Assemblers, compilers, and interpreters change high-level-language programs into assembly language or binary code that can run directly on the CPU.
programs
Computer programs retrieve input, transform information, and store output.
Computer programs are sequences of instructions. A complex instruction set has approximately 200 different instructions:
Read data (number, symbol, letter, word, date, or boolean) from a memory address into the CPU, or write data from CPU to a memory address.
Move data from a memory address to a register, or from a register to a memory address.
Using data retrieved from two registers, perform an arithmetic operation and put the resulting data in a register.
Using data retrieved from two registers, perform a logical operation (AND or OR) and put TRUE or FALSE in a register.
Using data retrieved from two registers, perform a comparison operation, to see if numbers are equal, less than, or greater than, or if strings are the same, different, longer, or shorter, and put EQUAL/SAME, MORE, or LESS in a register.
Depending on a condition (or unconditionally), branch to a new location in a program and perform the instruction there, sometimes returning to the previous location.
Transform strings or extract substrings from strings.
Determine if statement A and/or B is (NOT) true, and then perform statement C (conditional): "IF A, THEN C", "IF A AND B, then C", or "IF A OR B, then C".
If value of i is between m and n, perform x to change i, and then check value of i again (loop): "FOR i FROM m TO n, DO x".
Execute STOP instruction.
operation
The initial program loader starts the computer system by placing the operating system in memory and starting the central processor unit (CPU).
The operator routine loads the application program.
The data-management program inputs data and controls data flow.
The controller module controls operations, so the CPU executes the first instruction to retrieve, process, or write data.
The CPU continues following the program's instructions to the STOP program instruction. Computers must be able to get to at least one stop instruction and end program operation.
principles
Input data, instructions, intermediate results, and output data together make a state. Turing machines and computer systems have a finite number of states and go from initial state to final state.
Turing machines and computer systems go from state to state deterministically. Current state (instruction, intermediate result, and input) determines next state.
Positive integers can represent states. Turing machines and computer systems make integer series, which operate like algebras and are closed systems.
brains compared to computers
Neuron arrays can be computers [Eccles et al., 1976] [Pellionisz and Llinás, 1982].
Computers and brains have hardware and software: input data, data reading, computer memory, information processing, central processing unit, operating system, application programs, data writing, and output.
Brains and computers are integrated systems that store instructions, input, intermediate results, and output; read input and write output; process information using instructions, rules, and programs; and have states.
Brains combine features of analog and digital computers, because they have switches, clocks, continuous signals, thresholds, and multiple connections.
Brains combine features of serial and parallel computers, because many neurons simultaneously and continually read and write data according to instructions to many neurons.
Brains and computers have registers and memories that hold data, which can change.
Brains and computers have a central processing unit and operating system to run instructions and execute processes.
Mathematical Sciences>Computer Science
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Date Modified: 2022.0224