The Binary Number System Essay, Research Paper

The binary figure system is a system in which Numberss are represented as additive combinations of the powers of two. A binary figure is a figure written in base two. This means that each place in a numerical represents a peculiar power of two. In the more common decimal system, powers of 10s are used. A positive whole number is represented in base two by a line of nothing? s and one? s.The binary figure system is of import because of its application and value in computing machines. Digital computing machines constantly use the binary system. Computers code the denary figures into binary, while the strictly binary machines use full binary arithmetic. In the binary figure system, each figure represents a topographic point value. The first, ( from right to left ) represents the figure of units ; the 2nd, represents the figure of two? s ; the 3rd, the figure of 4s ; the 4th the figure of 8s, and so on. In this system every positive whole number is the amount of distinguishable powers of two, in merely one manner.

Base 2 Base 101 = 110 = ( 1*2 ) + ( 0*1 ) = 211 = ( 1*2 ) + ( 1+1 ) = 3100 = ( 1*2 ) + ( 0*2 ) + ( 0*1 ) = 41101001 = ( 1*2 ) + ( 1*2 ) + ( 0*2 ) + ( 1*2 ) + ( 0*2 ) + ( 0*2 ) + ( 1*1 ) = 10

In the binary figure system, every positive whole number is the amount of distinguishable powers of 2 in merely one manner.

The first twelve whole numbers are written as follows: Base Two/Base Ten & # 8230 ; & # 8230 ; & # 8230 ; & # 8230 ; & # 8230 ; & # 8230 ; & # 8230 ; & # 8230 ; & # 8230 ; 1 = 1 101 = 5 1001 = 9

10 = 2 110 = 6 1010 = 10 11 = 3 111 = 7 1011 = 11100 = 4 1000 = 8 1100 = 12

The advantages of the binary system prevarication in the fact that there are merely two sorts of binary figures, or spots, chiefly zero and one. This non merely gives a simplified arithmetic, but it provides a linguistic communication in which to handle two valued maps or bistable systems. A disadvantage of this system is the fact that it requires about three times as many figures to stand for a given

figure than does the denary system: The arithmetic operations for binary Numberss are simple. For add-on, merely 1+1 = 10 is needed, where as in the base 10 system, it is reduced to 1+1=2 or 1*1=1. 110101+ 11001 In any column 1+1=10.____________1001110

In decision to the binary figure system, it is largely used in digital computing machines for its ability to reassign denary figures to binary Numberss. The procedure is rather hard when confronted to our regular denary figures. Many people have found that utilizing the binary notation, or figure system, takes excessively much clip. Having two chief figures doesn? Ts make it easier to utilize. It merely takes up more clip. The binary figure system is fundamentally used with engineering related things like reckoners or computing machines. All in all, the binary notation/ Numberss are helpful. You merely have to cognize how to utilize it.

My OpinionThe double star figure system is a really confusing system as Is have come to larn through-out my research. I feel that although it involves less figures, that it creates more confusion about the Numberss that one has used. I did larn many things about the binary figure system or base two signifier, but I was unable to associate my findings to the Numberss on the wall. I would believe that they have to make with how they are arranged on the wall and how you would compose them in the binary figure system.

Bibliography

Williams, D Adams. ? Bartee Thomas C. Digital Computer Fundamentals. ? 6th edition New York. 1985. pages 296-297.

Oviatt, D Charles. ? Binary Notation. ? McGraw Hill Encyclopedia of Science and Technology. New York. 1987. page 497. vol. # 2.

Steven. Charles. ? Binary Number System. ? McGraw Hill Encyclopedia of Science and Technology. New York. 1987. pages 235-236.vol. # 12.

Miles, Jr. E.P. ? Binary Form. ? Encyclopedia Americana Grolier Inc & # 8230 ; Danbury, CT. 1997. page 751. vol. # 3.