This essay *The Binary Number System* has a total of 641 words and 5 pages.

The Binary Number System

The binary number system is a system in which numbers are represented as linear combinations of the powers of two. A binary number is a number written in base two. This means that each position in a numeral represents a particular power of two. In the more common decimal system, powers of ten are used. A positive integer is represented in base two by a line of zero’s and one’s.The binary number system is important because of its application and value in computers. Digital computers invariably use the binary system. Computers code the decimal digits into binary, while the purely binary machines use full binary arithmetic.

In the binary number system, each digit represents a place value. The first, (from right to left) represents the number of units; the second, represents the number of two’s; the third, the number of fours; the fourth the number of eights, and so on. In this system every positive integer is the sum of distinct powers of two, in just one way.

Base 2 Base 10

1 = 1

10 = ( 1*2) + (0*1) = 2

11 = ( 1*2) + (1+1) = 3

100 = ( 1*2 ) + (0*2) + (0*1) = 4

1101001 = ( 1*2 ) + (1*2 ) + (0*2 ) + (1*2 ) + ( 0*2 ) + (0*2) + (1*1) = 10

In the binary number system, every positive integer is the sum of distinct powers of 2 in just one way.

The first dozen integers are written as follows:

Base Two/Base Ten ...........................

1 = 1 101 = 5 1001 = 9

10 = 2 110 = 6 1010 = 10 11 = 3 111 = 7 1011 = 11

100 = 4 1000 = 8 1100 = 12

The advantages of the binary system lie in the fact that there are only two kinds of binary digits, or bits, mainly zero and one. This not only gives a simplified arithmetic, but it provides a language in which to treat two valued functions or bistable systems. A disadvantage of this system is the fact that it requires nearly three times as many digits to represent a given number than does the decimal system:

The arithmetic operations for binary numbers are simple. For addition, only 1+1 = 10 is needed, where as in the base ten system, it is reduced to 1+1=2 or 1*1=1.

110101

+ 11001 In any column 1+1=10.

____________

1001110

In conclusion to the binary number system, it is mostly used in digital computers for its ability to transfer decimal digits to binary numbers. The process is quite difficult when confronted to our regular decimal digits. Many people have found that using the binary notation, or number system, takes too much time. Having two main digits doesn’t make it easier to use. It just takes up more time. The binary number system is basically used with technology related things like calculators or computers. All in all, the binary notation/ numbers are helpful. You just have to know how to use it.

My Opinion

The binary number system is a very confusing system as i have come to learn through-out my research. I feel that although it involves less digits, that it creates more confusion about the numbers that one has used. I did learn many things about the binary number system or base two form, but I was unable to relate my findings to the numbers on the wall. I would think that they have to do with how they are arranged on the wall and how you would write them in the binary number 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... Danbury, CT. 1997. page 751. vol.#3.

## Topics Related to The Binary Number System

Binary arithmetic, Numeral systems, Computer arithmetic, Elementary arithmetic, Mathematical notation, Binary number, Positional notation, Hexadecimal, Power of two, Decimal, Binary, Scientific notation

## Essays Related to The Binary Number System