## How execute we Count utilizing Binary?

It is similar to counting in decimal other than we reach 10 lot sooner.

You are watching: What is -1 in binary

Well exactly how do us countin Decimal? | |||

0 | Start in ~ 0 | ||

... | Count 1,2,3,4,5,6,7,8, and then... | ||

9 | This is the last digit in Decimal | ||

10 | So us start back at 0 again, but include 1 ~ above the left |

The exact same thing is done in binary ...

Binary | |||

0 | Start in ~ 0 | ||

• | 1 | Then 1 | |

•• | 10 | Now start ago at 0 again, but add 1 top top the left | |

••• | 11 | 1 more | |

•••• | ??? | But now what ... ? |

What wake up in Decimal? | |||

99 | When we operation out the digits, us ... | ||

100 | ... Start ago at 0 again, but add 1 top top the left |

And that is what we execute in binary ...

Binary | |||

0 | Start in ~ 0 | ||

• | 1 | Then 1 | |

•• | 10 | Start earlier at 0 again, but add 1 top top the left | |

••• | 11 | ||

•••• | 100 | start ago at 0 again, and include one to the number on the left...... However that number is already at 1 for this reason it likewise goes back to 0 ...... And also 1 is added to the following position top top the left | |

••••• | 101 | ||

•••••• | 110 | ||

••••••• | 111 | ||

•••••••• | 1000 | Start ago at 0 again (for all 3 digits),add 1 top top the left | |

••••••••• | 1001 | And so on! |

See just how it is excellent in this little demonstration (press pat button):

## Decimal vs Binary

Here room some identical values:

### Symmetry

Binary numbers likewise have a beautiful and also elegant pattern:

## Position

In the Decimal device there are Ones, Tens, Hundreds, etc

In Binary there room Ones, Twos, Fours, etc, choose this:

This is 1×8 + 1×4 + 0×2 + 1 + 1×(1/2) + 0×(1/4) + 1×(1/8)**= 13.625 in Decimal**

Numbers deserve to be inserted to the left or best of the point, to display values higher than one and less than one.

10.1 | |

The number come the left of the point is a entirety number (such together 10) | |

As we move further left, every number placegets 2 times bigger. | |

The very first digit on the right means halves (1/2). | |

As we move more right, every number placegets 2 time smaller (half together big). |

### Example: 10.1

The "10" method 2 in decimal,The ".1" means half,So "10.1" in binary is 2.5 in decimalYou can do conversions in ~ Binary come Decimal come Hexadecimal Converter.

## Words

The word **binary** originates from "Bi-" definition two. We watch "bi-" in native such as "bicycle" (two wheels) or "binocular" (two eyes).

When you say a binary number, pronounce each digit (example, the binary number "101" is talked as "one zero one", or sometimes "one-oh-one"). This means people don"t get puzzled with the decimal number. |

A single binary number (like "0" or "1") is dubbed a "bit".

For example **11010** is 5 bits long.

See more: The Pit And The Pendulum Quotes, By Edgar Allan Poe

The word** bit** is consisted of from the native "**b**inary dig**it**"

## How to display that a Number is Binary

To present that a number is a binary number, monitor it with a small 2 choose this: **1012**

This way people won"t think that is the decimal number "101" (one hundred and also one).

## Examples

### Example: What is 1111**2** in Decimal?

The "1" on the left is in the "2×2×2" position, for this reason that way 1×2×2×2 (=8)The following "1" is in the "2×2" position, therefore that means 1×2×2 (=4)The next "1" is in the "2" position, so that means 1×2 (=2)The last "1" is in the people position, for this reason that way 1Answer: 1111 = 8+4+2+1 = 15 in Decimal### Example: What is 1001**2** in Decimal?

The "1" top top the left is in the "2×2×2" position, so that way 1×2×2×2 (=8)The "0" is in the "2×2" position, for this reason that method 0×2×2 (=0)The next "0" is in the "2" position, for this reason that way 0×2 (=0)The last "1" is in the people position, therefore that means 1Answer: 1001 = 8+0+0+1 = 9 in Decimal### Example: What is 1.1**2** in Decimal?

The "1" on the left next is in the ones position, for this reason that means 1.The 1 top top the appropriate side is in the "halves" position, therefore that method 1×(1/2)So, 1.1 is "1 and 1 half" = 1.5 in Decimal### Example: What is 10.11**2** in Decimal?

The "1" is in the "2" position, so that means 1×2 (=2)The "0" is in the persons position, therefore that method 0The "1" ~ above the ideal of the allude is in the "halves" position, for this reason that means 1×(1/2)The last "1" top top the best side is in the "quarters" position, so that method 1×(1/4)So, 10.11 is 2+0+1/2+1/4 = 2.75 in Decimal"There are 10 kinds of world in the world,those who recognize binary numbers, and those who don"t."

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