Lesson 2 logical circuit elements

1. We pointed out that any digital calculation — whe­ther it be performed by ‘pencil and paper’ methods or with the aid of an automatic computer — must first be broken down into a sequence of elementary arithmetical operations, such as addition or multiplication. The pro­cess may be taken a stage further; each such arithmeti­cal operation may be analyzed into a sequence of simple logical operations. To this end, it is con­venient to make use of some techniques derived from the field of symbolic logic and of a diagrammatic notation derived from the field of neurology. The link between three such apparently dissimilar disciplines is that each is concerned with two state elements. A binary digit — and its physical embodiment — may take only two values, ‘0’ and ‘1’; a logical proposition may be either true or false; an individual nerve cell is capable only of an ‘all-or-none’ response, not of a graduated response.

2. A symbolism and a set of rules suitable for manipu­lating 'yes or no' logical propositions was developed by George Boole (1815—64), a sell-educated genius who be­came Professor of Mathematics at Cork University in the middle of the nineteenth century. The techniques of Boolian algebra, as the subject is called, are now extensively used — following the pioneer work of Shannon at the Bell Telephone Laboratories in 1938 — by electrical engineers for the design and analysis of switching circuits. Both the arithmetic and control units of an automatic compu­ter consist essentially of assemblages of switching cir­cuits for routing and manipulating electrical pulse sig­nals, and so it is not surprising that Shannon 's approach has found ready acceptance among computer designers.

3. The process of combining a number of electronic cir­cuits of known logical properties into an integrated system capable of performing specified arithmetical or control functions is known as logical design.

Exercise 1. Find the synonyms in the text to the following words:

1. computation (1) 6. originate (1)

2. to be carried out (1) 7. to deal with (1)

3. with the help (1) 8. clearly , strictly (1)

4. sphere (1) 9. mainly (2).

5. answer (1)

Exercise 2. Give the Ukrainian equivalents to the following words and phrases:

1. digital;

2. addition and multiplication;

3. sequence of operations;

4. symbolic logic;

5. neurology;

6. binary digit;

7. self-educated genius;

8. pioneer work;

9. pulse signals;

10. switching circuits.

Exercise 3. Say if the statements are true or false:

1. A symbolism and a set of rules suitable for manipulating ,,yes” or ,,no” logical propositions was developed by Shannon at the Bell Telephone Laboratories.

2. Addition and multiplication are the simplest arithmetical operations.

3. Some techniques in the field of symbolic logic are derived from the science of neurology.

4. All units of automatic computer consist of switching circuits.

5. A binary digit may take only three values “0” , ,”1” and “10”.

Exercise 4. Complete the sentences choosing the right variant:

1. Both the arithmetic and the control units consist of switching circuits for… electrical pulse signals.

a). positioning and contouring;

b). routing and manipulating;

c). coding and decoding.

2. Any digital calculation must be broken down into:

a). sequence of reasonable operations;

b). sequence of logic operations;

c). sequence of arithmetical operations.

3. Physical embodiment of a binary digit may take only two…

a). figures;

b). values;

c). signs.

4. The techniques of Boolean algebra are used by electrical engineers for design of…

a). electronic circuits

b). switching circuits

c). integrated circuits.

5. It is not surprising that Shannon’s approach has found acceptance among…

a). electrical engineers

b). logical designers

c). computer designers.

Exercise 5. Answer the following questions:

1. What should be done first working with any digital calculation?

2. Why is it convenient to use some methods of symbolic logic and diagrammatic notation, derived from the field of neurology?

3. A logic proposition is either true or false, isn’t it?

4. Who developed symbolism? Was this person the pioneer in this field?

5. Why has Shannon’s approach found acceptance among computer designers?

Exercise 6. Define the notation ,,logical design”.

Exercise 7. Describe how any digital calculation is performed.

Exercise 8. Explain why there is a link between symbolic logic, diagrammatic notation, neurology.

Exercise 9. Discuss the text according to the points:

1. Sequence of logical operations.

2. Two values of a binary digit.

3. The techniques of Boolean algebra.

Notes:

1. convenient – зручний

2. dissimilar – несхожий

3. embodiment – втілення

4. proposition – ствердження (теорема мат.)

5. nerve cell – нервова клітина

6. all – or – none – response – відповідь “так ” чи “ні ”.

7. assemblages – зборка, монтаж

8. approach – підхід

9. properties – властивості.