What is binary system?

0 votes
in Mathematics by
What is a binary system, please put it in plain words to explain me clearly?

7 Answers

0 votes
by
Binary is a numeric system that uses two numerals to represent all real numbers. While the most common counting system, the decimal system, uses ten numerals, binary uses only 0 and 1.

Each digit in a binary number system, therefore, represents a power of two. The first digit on the right represents the 0th power, the second represents the 1st power, the third represents the 2nd power, and so on. So the number 1 in the decimal system is represented also as 1 in the binary system. The number 23, by contrast, is represented as 10111 (16+0+4+2+1).
0 votes
by
numeration system based on powers of 2, in contrast to the familiar decimal system, which is based on powers of 10. In the binary system, only the digits 0 and 1 are used. Thus, the first ten numbers in binary notation, corresponding to the numbers 0,?1,?2,?3,?4,?5,?6,?7,?8, and 9 in decimal notation, are 0,?1,?10,?11,?100,?101,?110,?111,?1000, and 1001. Since each position indicates a specific power of 2, just as the number 342 means (3 נ102) + (4 נ101) + (2 נ100), the decimal equivalent of a binary number can be calculated by adding together each digit multiplied by its power of 2; for example, the binary number 1011010 corresponds to (1 נ26) + (0 נ25) + (1 נ24) + (1 נ23) + (0 נ22) + (1 נ21) + (0 נ20) = 64 + 0 + 16 + 8 + 0 + 2 + 0 = 90 in the decimal system. Binary numbers are sometimes written with a subscript "b" to distinguish them from decimal numbers having the same digits. As with the decimal system, fractions can be represented by digits to the right of the binary point (analogous to the decimal point). A binary number is generally much longer than the decimal equivalent; e.g., the number above, 1011010b, contains seven digits while its decimal counterpart, 90, contains only two. This is a disadvantage for most ordinary applications but is offset by the greater simplicity of the binary system in computer applications. Since only two digits are used, any binary digit, or bit, can be transmitted and recorded electronically simply by the presence or absence of an electrical pulse or current. The great speed of such devices more than compensates for the fact that a given number may contain a large number of digits.
0 votes
by
The number system we are used to using is the decimal system, also known as base 10. It's called that because of what each digit represents in a number:

573 = 5 * 10^2 + 7 * 10^1 + 3 * 10^0

(5 hundred, 7 tens, and 3 ones)

The binary system, on the other hand, is base 2. It only has the digits 0 and 1. For example,

11001 = 1 * 2^4 + 1 * 2^3 + 0 * 2^2 + 0 * 2^1 + 1 * 2^0

(1 sixteen, 1 eight, 0 fours, 0 twos, and 1 one)

Therefore, 11001 in binary translates into 25 in decimal.
0 votes
by
the binary is when you only get two possible digits in your digit system. not 10 as we have - 0 1 2 3 4 5 6 7 8 9, but just 0 and 1. so 0 is 0, 1 is 1 and then you do what you do in 10 digit system, if run out of digits you make a new decimal place. so 2 is 10 and 3 is 11 and 4 is 100. you can also think of their digits and powers of 2. so you got ex. 4 of 100 there is just one 2^2 and 0 1^2 and 0 of 0. 16 if 10000.-  only one of 2^4. 17 is 10001 we also needed one of 1s.
0 votes
by
The binary numeral system, or base-2 number system, is a numeral system that represents numeric values using two symbols, usually 0 and 1. More specifically, the usual base-2 system is a positional notation with a radix of 2. Owing to its straightforward implementation in digital electronic circuitry using logic gates, the binary system is used internally by all modern computers.
0 votes
by
The binary system, or base two systems, is a system used to express numbers using only the digits 1 and 0.

The decimal system, or base ten systems, (the system we commonly use), uses the digits 0,1,2,3,4,5,6,7,8,9, and each digit has a different value depending on the position it has in a number.  For instance, figure 258 in the decimal system means eight units, plus five tens, plus two hundred. Each position corresponds to a power of ten, 1,10,100,1000,10000, etc.

The binary system is similar in that each digit has a different value depending on the position it has in the number. In the binary system, however, each position corresponds to a power of two 1,2,4,8,16,32, etc, not to a power of 10. And, as said before, it uses only two digits: 1 and 0. For instance, the decimal numbers from zero to ten would be in binary

0

1

10

11

100

101

110

111

1000

1001

1010

It is possible to express numbers in any base. The rule is the same, you use the first n digits (starting from zero) and each position corresponds to a power of the base. For instance, numbers zero to ten in base three would be:

0,1,2,10,11,12,20,21,22,100,101

When the base is greater than 10, you need to begin using letters beside the traditional digits 0-9. Base 16 for instance is commonly used in computer programming, and It uses 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F
0 votes
by
our normal system is what they call a 10 base, 0-9, binary is a 2 base, 0-1.  what this means instead of counting to 9 then adding a "tens" place, we count to one, then add a digit representing counts of 2.

for instance, 17 is easy to write out for 10 bases when used to it.  17 in binary is 10001.  as with the place values where 100 one value of one hundred+ zero values of ten+zero values of 1.  17 is 1 value of 16+zero values of 8,4,2,+one value of one.

16+8+4+2+1

1     0  0   0  1
...