Lecture № 1. 3. Calculation systems. Binary calculation system

the trigger. The trigger is an electric element which can

be in two steady conditions: it is included or switched off, it is similar to the switch.
The COMPUTER is constructed on a binary calculation system, each of conditions of the trigger can compare 0 or 1. In both conditions the trigger is stable, that gives to the binary in-formation stored it very high reliability. There are also other ad-vantages of a binary calculation system. Transfer of the informa-tion to a computer is carried out by means of transfer of electric impulses. Characteristics of an electric signal are force of a cur-rent and a pressure. On electric signals the big influence is ren-dered with the handicapes created by external electromagnetic fields. Electric signals in a computer as are subject to handicapes and importance of these handicapes much more, than at radio or a telecast where because of flickering strips on the screen, nevertheless it is possible to make out the image. How this prob-lem is solved in a computer? Due to a binary calculation system.

magnetic carrier. The basic properties of a magnet are polarity

and a level of magnetization. There are two conditions of magnetization of magnet SN and NS. So, conditions two, therefore it is possible to compare with polarity of magnet SN with 0, and NS with 1. Thus, have received system of storage of the binary information. The magnet has one more easily changeable property which can bear the helpful information. We shall admit, we shall compare with the certain levels of magnetization to figures of a decimal calculation system. Thus, it is possible to write down numbers in decimal system by means of sequence of magnets. A level of magnetization very astable characteristic subject to influence of external magnetic fields (an example the deteriorated record on an old magnetic tape can serve). For change of polarity of a magnet much stronger magnetic field is required. The information from a diskette not

strong magnet. It is caused by use on floppy disks

as a data carrier property of a magnet - magnetization. The size "1" so strongly differs from "0", that spontaneous change of magnetization (or under action of external magnetic fields) is so insignificant (concerning a level "1"), that the probability of loss of the information is close to 0. On compact discs as the binary system of record-storage is used. As zero (0) deepenings, burned on a smooth surface of a disk there act. The nature represents us advantages of use of binary system of calculation where reliability of storage is very high.
Each such set of zero and units refers to as a binary code. The quantity of the information coded in binary figure - 0 or 1 - refers to bat. By means of a bats set, it is possible to present any number and any sign. Signs are represented by eight-digit bats combinations – by bytes (i.e. 1 byte = 8 bats). For example, the Russian letter A – 10000000 byte. Any bats combination can be interpreted as number. For example, 110 means number 6, and 01101100 - number 108. The number can be presented by several bytes.

two. Any numbers in this system are represented by sequence

of figures 0 and 1. Thus each senior category more next younger twice.
For example, binary number 10101 in the developed kind can be written down so:
1*24+0*23+1*22+0*21+1*20
For reception of value of binary number 10101 in a binary calculation system it is enough to calculate the written expression:
1*24+0*23+1*22+0*21+1*20=16+0+4+0+1=21
The fractional binary number in the developed kind enters the name with use of positions with negative numbers.
For example, 101 in the developed kind will enter the name:
1*22+0*21+1*20=4+0+1=5

shall specify as the bottom index at the most right

figure of number, for example: 12510 - a decimal calculation system; 10112 - a binary calculation system.
In a binary calculation system the whole decimal numbers from zero up to nine are accordingly represented so:

addition is carried out with use of the table of

binary addition in one category:
10012 11012 111112
+ 10102 + 10112 + 12
100112 110002 1000002

2. Operation of subtraction is carried out with use of the table of subtraction in which 1 the loan in the senior category is designated.
1011100112 1101011012
–1000110112 – 1010111112
0010110002 0010011102

scheme applied in decimal calculation system with consecutive multiplication of

the 1-st multiplier on the next figure of the 2-nd multiplier.

х 110012 х 1012
11012 112
11001 101
11001 101 .
11001 11112
1010001012

similar to algorithm of operation of division in decimal calculation

system.
– 1010001012 | 11012 – 1000110002 | 11112
1101 110012 1111 100102
- 1110 - 0010100
1101 1111
– 1101 10102 – a remainder of
1101 division
0