### Understanding Digital Computers

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Inventory control is a complex and varied procedure, but the key questions can be formulated in mathematical equations where numerical quantities are substituted to describe an inventory situation as it actually exists.

## Digital computer

Some means must be available, then, to get these numerical quantities into the computer. This requires an input facility that converts any symbols used outside the machine numerical, alphabetical or otherwise into the proper internal code used by the machine to represent those symbols. Generally, the internal machine code is based on the two numerical elements 0 and 1. In the decimal-number system, each symbol from 0 through 9 is called a digit.

As we move one place from right to left in this system, we are multiplying by a factor of In the 0- and -1 system—described as binary—each symbol—0 or 1—is called a "bit," which is a contractor of the words "binary" and "digit. The 0's and 1's of binary notation represent the information processed by the computer, but they do not appear to the machine in that form. They are embodied in the ups and downs of electrical pulses and the settings of electronic switches inside the machine. For an understanding of pulse-formation and pulse sequences, it may be helpful to consider an elementary circuit consisting of a battery say, a 6-volt type , a light bulb and a spring-loaded hand key, all connected, with the operator alternately pressing down on the key and releasing it.

When the key is down, the battery voltage turns on the light with a 6-volt pulse. When the key is released, the lamp voltage becomes 0 and the light goes off.

When the key is pressed again, there is another 6-volt pulse and the lamp lights again. If the hand on the key were steady and the sequence rhythmical, the pulses would occur regularly and distributed evenly along an imaginary base line whose length represented time.

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The width of the space occupied by each pulse would depend on the beat, or frequency. Since the pulses given off by our pulse-producer are either 6 volts or 0, we could call the 6-volt level of each pulse a 1 and the level at which there is no voltage a 0. In effect, then, we can use pulses as the conveyors of information. Such pulses can be used to code decimal numbers, alphabetic letters, words, punctuation marks or designs arranged in machine-readable patterns.

Some advanced inputs involve the scanning of a printed page, the conversion of a limited vocabulary of spoken words and the use of "light pens" to detect information on a television-like cathode-ray tube. So far as our inventory equation is concerned, the information pertaining to it may be inserted in the computer by any of a variety of input devices. One possible device is actually a key-driven machine—a typewriter whose keys are connected to electronic networks that convert information into pulse sequences corresponding to notations on the pressed keys.

Such terminal devices may be operated at remote points. Other input means are provided by punched cards and punched tape, with metal brushes or photoelectric cells sensing the holes and closing an electric circuit each time a hole is sensed. Use is also made of magnetic tape, disks, drums and ink, with the information being represented by different patterns of magnetized spots. Look at one of your bank checks.

The chances are you will find some numerals at the bottom. They are printed with magnetic ink for purposes of data processing. But getting back to the inventory problem. Once the information pertaining to it is fed into the machine, the data must be lodged somewhere and preserved so that they do not disappear.

For example, when a computer is "told" how many inventory items are on hand, it must "remember" that fact—and other facts associated with the problem. Storing such information is the function of the computer "memory. Magnetic tape, disks and rotating drums are used as auxiliary memories.

## Understanding Digital Computers - PDF Free Download

On such auxiliary devices, information is recorded and retrieved from their surface by "read-write" heads similar to those used for the recording and playback functions on an ordinary tape recorder. A core, whose dimensions are measured in thousandths of an inch, is a tiny doughnut-shaped object pressed from a mixture of ferric oxide powder and other materials and then baked in an oven.

Millions of cores are used for very large computer memories. They are strung, or "sewn," into a wire mesh. Then other wires are passed through them in three planes so that appropriate pulses can cause each core to absorb "read" or release "write" information bits. E lectric current is sent through the wires to magnetize a core. Even if the current is removed, the core remains magnetized in the same direction. It stays magnetized in this way until reversal of the applied current causes it to change state. The two states can be used to represent 0 or 1, plus or minus, yes or no, on or off.

With so many cores strung together, how is a particular core selected for storing a bit? Two wires run through each core at right angles to each other. Only half the current required to magnetize a core is sent through each wire. Consequently, only that core receiving full magnetization current from the two wires is selected.

When a core is required to release information, a "read" current is applied to it. This causes a change in its state, and the change induces a pulse in the sense wire that amounts to a message from the memory to another part of the computer. For rotating drums, the read-write heads contain coils of fine wire wound around tiny magnetic elements.

A channel drum used for storage in a data-processing system, with seven formation tracks for each channel. Means have now been described for getting information into the computer and storing it. Since problems like inventory control are based on equations, however, the computer must at least have the arithmetic capability of adding, subtracting, multiplying and dividing. In manipulating numerical data inside the computer, it is necessary to shift bits of information or hold while parts of the machine analyze the data.

Sometimes it is also necessary to compare two numbers to see if they are equal, or to see if one is larger than the other, or if it is 0, and so on. Indeed, many modern computers provide more than a hundred capabilities such as these, each one of which is built into the hardware. Its physical parts include various registers, comparators, adders, and other "logic circuits. A register is a device that receives information, holds it—usually temporarily—and then releases it as directed by the step-by-step instructions programmed into the computer.

Magnetic cores or "flip-flops" are frequently used to form a register. A flip-flop is an electronic switch. It usually consists of two transistors arranged so that incoming pulses cause them to switch states alternately. One flips on when the other flops off, with the latter releasing a pulse in the process.

Thus, multiple flip-flops can be connected to form a register in which binary counting is accomplished by means, of pulse triggers. Stable two-state electronic devices like the flip-flop are admirably suited for processing the 0 and 1 elements of the binary-number system. This, in fact, helps to explain why the binary-number system is commonly used in computers. Like decimal numbers, binary numbers obey all the rules of arithmetic and can therefore be added, subtracted, multiplied and divided.

Addition is the primary arithmetic process carried out in the computer's arithmetic-logic unit. All of the operations can be carried out either by addition or variants of addition.

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For example, multiplication can be done by repeated addition. Subtraction can be accomplished by complementing one number, adding it to another and then adding an extra 1. And division can be achieved by repeated subtraction. The complement of 88, for example, is In the binary system, the complement of a number is obtained by subtracting that number from a series of 1's and then adding the extra 1. This, however, is equivalent to changing all 0's to 1's and all 1's to 0's and then adding 1.

## Tandy/Radio Shack Book: Understanding Digital Computers (1978)(Radio Shack)

Consequently, in a computer, it is easy to provide simple circuitry to complement a number by inverting it and, in this way, carry out subtraction by means of addition. Basic operations in the binary system, similar to those carried out in the decimal system. A bar over any symbol means NOT. If another switch is in series with the first switch and its two states are similarly considered to be B for closed and NOT B for open, then we must have both an A and B for the entire circuit to be completed. When the A and B conditions are met the result may be called "true" or 1.

Thus, for the two switches in series, the completed circuit may be described, by the simple Boolean equation: A x B. Use of the Boolean notation may be illustrated in the design of the familiar upstairs-downstairs light arrangement in which a hall lamp can be turned on or off from either location. The four conditions implicit in the problem may be represented in logic diagrams or, even more effectively, in a "truth table. In handling the logic required to process a problem like inventory control, the computer is obviously dealing with more complicated matters than the hall lamp arrangement.

A gate is a logic element that produces an output signal only when a specified set of conditions is met. If the conditions are met, the gate will pass information pulses; if not, it will block the flow. There are three basic types of gates: the OR, which passes data when the appropriate signal is present at any of its inputs; the AND, which passes data only when the same appropriate signals are present at all inputs; and the NOT, which turns a 1-signal into a 0-signal, and vice versa.

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Gates are package elements in computers. The best example of the analog device will be oscilloscope which is still used by engineers for taking measurements. While the best case of Digital devices will be a pedometer which gives the exact number of steps.