How does the binary number system use only 1s and 0s to represent numbers?.?

Question

How does the binary number system use only 1s and 0s to represent numbers ?

Answer 1

The binary numeral system (base 2 numerals) represents numeric values using two symbols, typically 0 and 1. More specifically, the usual binary numeral system is a positional notation with a radix of 2. Owing to its straightforward implementation in electronic circuitry, the binary system is used internally by virtually all modern computers. A binary number can be represented by any sequence of bits (binary digits), which in turn may be represented by any mechanism capable of being in two mutually exclusive states. The following sequences of symbols could all be interpreted as the same binary numeric value:

1 0 1 0 0 1 1 0 1 0
| - | - - | | - | -
x o x o o x x o x o
y n y n n y y n y n

The numeric value represented in each case is dependent upon the value assigned to each symbol. In a computer, the numeric values may be represented by two different voltages; on a magnetic disk, magnetic polarities may be used.

A "positive", "yes", or "on" state is not necessarily equivalent to the numerical value of one; it depends on the architecture in use.
In keeping with customary representation of numerals using Arabic numerals, binary numbers are commonly written using the symbols 0 and 1. When written, binary numerals are often subscripted, prefixed or suffixed in order to indicate their base, or radix. The following notations are equivalent:

100101 binary (explicit statement of format)
100101b (a suffix indicating binary format)
100101B (a suffix indicating binary format)
bin 100101 (a prefix indicating binary format)
1001012 (a subscript indicating base-2 (binary) notation)
%100101 (a prefix indicating binary format)
0b100101 (a prefix indicating binary format, common in programming languages)

The first Wikipedia link will give you further information on:
* History,
* Representation,
* Counting in binary
* Binary simplified
* Binary Arithmetic (Addition, Subtraction, Multiplication, Division)
* Bitwise logical operations
* Conversion to and from numeral systems

The second link is regarding Computer numbering formats, the third is provided to help you in understanding of conversion of factors, fourth is the explanation of two’s complement, the fifth regarding the most significant bit, the sixth explains the least significant bit, next comes signed number representation followed by unsigned numbers and finally the sign bit. Hope this is enough for the time being to get you started….

Answer 2

Because we are limited at this time by electronic systems that use on/off as the only way to store information. Engineers use the digital system for everything but computers, and for those they use the octal(8) and hexadecimal(16) system too. A silly example of other systems are the British/American measurements, just ask anyone how many inches and yards in a mile, teaspoons in a gallon, and why a ton is the same in metric and US standards. Nature does the binary system (male/female) along with any others it can find (DNA could be viewed numerologically) Because a person has ten fingers, the decimal system comes naturally and is easy to learn. Other number systems work as well but are a pain to learn, otherwise there is nothing wrong with them. (some code writers are able to do complex computations using either 2,8,16,or 10 based systems in their heads, it just takes practice)

Answer 3

Binary uses more digits to show higher value numbers, like we do with decimal, only the greater digits have different values.

It goes (with eight digits)
128 64 32 16 8 4 2 1
(see a pattern? The next digit is double the previous)

So 0001 equals 1, 0010 equals 2, 0100 equals 4.

To get the in between numbers, add the values if the digit equals one:

0011 equals 3 (2+1), 0101 equals 5 (4+1), 1011 equals 11 (8+2+1)

Addition is a little different, when you add, 0+0=0, 1+0=0, 1+1=0 carry 1

So 1 + 2:
0001
0010+
-------
0011

2+2:
0010
0010+
-------
0100

4+6:
0100
0110+
-------
1010

Answer 4

Its complicated yet simple at the same time. 1 means on, 0 means off. Then if you have an 8bit binary number, you add those that are on up.

128,64,32,16,8,4,2,1
0 1 1 0 1 0 0 1

Given the above, I can add up just those bits that are on in this equation: 64 + 32 + 8 + 1 = 105

Answer 5

Simply by counting.

A bit is 0 or 1. So, if I have two bits, I can count to 3:

00 = 0
10 = 1
01 = 2
11 = 3

If I have three bits, I can count to 7:

000 = 0
100 = 1
110 = 2
111 = 3
010 = 4
011 = 5
001 = 6
101 = 7

etc., etc.

Answer 6

The ways the ones and zeros are set up in combinations.

Answer 7

Take a look here

http://en.wikipedia.org/wiki/Binary_number_system

Answer 8

Read this- http://britton.disted.camosun.bc.ca/jbbinary.htm