Digital computer and logic design?
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Yes, they go together.
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you will find everything you want here:\n\nhttp://en.wikipedia.org/wiki/Logic_gates
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digital design.\nor communications.\n\nprepare for alot of electrical.
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Logic circuits built out of transistors. Those transistors are today built into an IC chip. The most important circuits for the calculator are the 'full adder' circuit, and various memory circuits.
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Electronic engineering
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You can buy them in chip form. I think Analog Devices makes them, up to eight bit. They are easier to use and more accurate than anything ou could build from discrete parts.
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In the 1940's with ENIAC.  It was one of the first "high-speed" computational devices and is considered the first major milestone in the development of digital computers.  It was used mainly by the U.S. military during WWII for artillery trajectory calculations.\n\nHowever things really took off after the development of the silicon transistor (1954), which are still in use today.
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the development of the transistor --  Bell Laboratories --  1947
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Hardware and software.
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why do not you tyr this link \n\nhttp://www.tekxam.com/StudyGuide/concepts/General-Concepts/General_Computing_Concepts_OUTLINE.html
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Ummm...that is probably not going to find an intelligent answer in "Programming & Design".  Try re-posting this in say, "Society & Culture" and you may get an intelligent answer.
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the "software" is the languages such as verilog and vhdl\n\nthe code is firsts compiled \nthen the product is called a structural netlist.\nthen the netlist is run thru a synthesis program, ie synplicity, leonardo, percision synthsis, or design compiler.\nthis process converts the code into logic gates, with timing delays,\ncapacitances, and resistances.\nthen the netlist is send to floorplanning, for place and routing.\nthats the rough outline.
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Intel has online data books. These are helpful in programming, interfacing, sample code as well as hardware information.
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Boolean logic is a complete system for logical operations. It was named after George Boole, an English mathematician at University College Cork who first defined an algebraic system of logic in the mid 19th century. Boolean logic has many applications in electronics, computer hardware and software. In 1938, Claude Shannon showed how electric circuits with relays were a model for Boolean logic. This fact soon proved enormously consequential with the emergence of the electronic computer.\n\nLogic design is based on Boolean. It works on the concept of an ON and OFF stae or 1 and 0.
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Mathematics makes significant contributions to IT, supporting the development of both hardware and software systems. Some examples of maths that have specific application to IT (in a digital as opposed to analogue computer) are:\n\nBoolean logic:\n\nThis is a system of mathematics based around the binary states True and False (represented typically as non zero and zero). A number of basic logical operations are defined from which infinitely more complex logical rules can be built. These operations are defined in terms of inputs and outputs, and the effects can be shown by truth tables. The basic logical operations are:\n    NOT (negation)\n         Input    Output\n             T          F\n             F          T\n     OR (either or both inputs may be True)\n         Input1  Input2   Output\n             T           F          T\n             F           T          T\n             T           T          T\n             F           F          F\n     AND (both inputs must be true)\n         Input1  Input2   Output\n             T          T           T\n             T          F           F\n             F          T           F\n             F          F           F\n     XOR (one and only one input is true)\n          Input1  Input2   Output\n             T          T           F\n             T          F           T\n             F          T           T\n             F          F           F\n\nThe application of this to IT may not be immediately apparent, but this system of logic underpins both the design of the microprocessor in modern personal computers and the means to implement decision making in programming. Rules such as the following can be constructed:\n\nIf (AuthorAlive = True) AND (AuthorNotPaidEnough = True) Then GiveAuthorPayRise\n\nBinary representation:\n\nBinary is a system of mathematics based around the presence of only 2 numbers, 0 and 1. Where we have a tens column in decimal, this becomes a twos column in binary, the hundreds column becomes a fours column, the thousands column and eights column, and so on. Both processing and data storage devices in a digital computer work on a binary system at the lowest level and this has important ramifications for the capabilities of the computer.\n\nWe frequently refer to a single binary digit as a bit. Ultimately all bandwidth and data storage capacities are measured in bits, because this is the fundamental unit a computer works on. The internal limitations of a computer are derived from properties of binary mathematics.\n\nThe reason that a digital computer is built on base 2 representation is that it is much easier to construct systems with 2 stable states as opposed to more. This can correspond to the presence or absence of voltage, a north versus south pole magnetic field, a True or False boolean value in a logic gate and so on.\n\nAdditionally:\n\nThere are a lot of mathematical problems or modelling that are represented using computers. The very early origins of the computer were heavily driven by their application as calculating machines (to calculate the trajectory of artillery shells, for instance).\n\nAlso, as with any modern engineering, the field of mathematics heavily underpins IT at the physical level, through physics. We could not design a modern computer without the application of a lot of physics and therefore Maths.\n\nTherefore, this really is a very open wide ranging question.
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binary generation or backtracking techniques
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A memory chip allows you to store & retrieve data.  A logic chip performs a function on given data.\n\nFor example, a logic chip designed to be an Adder would take in two inputs and return one output (the addition of the two numbers).