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?
0Start in ~ 0
...Count 1,2,3,4,5,6,7,8, and then...
9This is the last digit in Decimal
10So us start back at 0 again, but include 1 ~ above the left

The exact same thing is done in binary ...


Binary
0Start in ~ 0
1Then 1
••10Now start ago at 0 again, but add 1 top top the left
•••111 more
••••???But now what ... ?

What wake up in Decimal?
99When 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
0Start in ~ 0
1Then 1
••10Start earlier at 0 again, but add 1 top top the left
•••11
••••100start 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
••••••••1000Start ago at 0 again (for all 3 digits),add 1 top top the left
•••••••••1001And so on!

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

Decimal vs Binary

Here room some identical values:


Symmetry

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Binary numbers likewise have a beautiful and also elegant pattern:

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Position

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

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

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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
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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.
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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 decimal

You 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).


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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 "binary digit"


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 11112 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 10012 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 1.12 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 10.112 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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