# Powers of Two Generator

## World's Simplest Number Tool

Quickly generate a sequence of powers of two in your browser. To get your series, just specify the starting value and how many series members you need in the options below, and this utility will generate that many powers of two. Created by developers from team Browserling.

Tool Options

#### Start, Length and Separator

Start generating powers of
two from this value.
Generate this many powers
of two.
Separate powers of two by this
symbol. (By default newline.)

#### Order of Series

Generate powers of two in
the positive direction.
For example: 2⁰, 2¹, 2², ...
Generate powers of two in
the negative direction.
For example: 2⁰, 2⁻¹, 2⁻², ...
For positive powers of two,
subtract one but for negative
add one. (Try in binary mode
to see the effect!)

#### Powers of Two Output Base

Enter the custom base here.
(Works from 2 - 64.)

## What Is a Powers of Two Generator?

This is an online browser-based utility for generating a list of numbers that are powers of two. A number is a power of two if it is calculated by raising the number 2 to an integer power. When the power is positive, all powers of two are also positive integers. The first three values of powers of two list are 2¹ = 2, 2² = 4, 2³ = 8. When the power is negative, the result is positive but no longer an integer, it's now a decimal fraction. It's greater than zero but less than one. The first three values when the power is negative are 2⁻¹ = 0.5, 2⁻² = 0.25, 2⁻³ = 0.125. With this tool, you can calculate a sequence with both positive and negative power values. You can specify the starting power of two value, the number of sequence elements, and which symbol to separate terms with. Often in programming and computer science, you need values one-less than the exact power of two, so we also added an option to generate series members in the form 2^n-1. As a bonus, you can also convert the series to any radix (base). That's absolutely numberwang!

## Powers of Two Generator Examples

Click to try!

### First Thirty Powers of Two

In this example, we generate the first thirty powers of two with positive powers. We start with x=1 and calculate 2^x = 2¹ = 2. Then we increase x to 2 and calculate the next value, which is 2² = 4. We keep increasing x by one until it's 30 and the series we get is (2¹, 2², 2³, 2⁴, ...).

2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912, 1073741824
Required options
These options will be used automatically if you select this example.
Start generating powers of
two from this value.
Generate this many powers
of two.
Separate powers of two by this
symbol. (By default newline.)
Generate powers of two in
the positive direction.
For example: 2⁰, 2¹, 2², ...
For positive powers of two,
subtract one but for negative
add one. (Try in binary mode
to see the effect!)

### Descending Order

In this example, we generate a list of powers of two in descending order. The first value in the list is 2⁰. Then we decrease the power by one and all the following powers are negative (2⁻¹, 2⁻², 2⁻³, ...). When raising a positive integer to a negative power we get a decimal fraction. Let's look at the first negative power of two; for this power 2⁻¹ = 1/2¹ = 1/2 = 0.5. Similarly for the second negative power of two, we get 2⁻² = 1/2² = 1/4 = 0.25. For the third – 2⁻³ = 1/2³ = 1/8 = 0.125. As you can see, the list of negative powers decreases but it never reaches zero.

1 0.5 0.25 0.125 0.0625 0.03125 0.015625 0.0078125 0.00390625 0.001953125
Required options
These options will be used automatically if you select this example.
Start generating powers of
two from this value.
Generate this many powers
of two.
Separate powers of two by this
symbol. (By default newline.)
Generate powers of two in
the negative direction.
For example: 2⁰, 2⁻¹, 2⁻², ...
For positive powers of two,
subtract one but for negative
add one. (Try in binary mode
to see the effect!)

### 2^x-1 in Binary Base

In this example, we generate a sequence of powers of two minus one, or in mathematical notation 2^x-1. We also change the base of the output sequence to binary to show you its nature. By converting the results to the binary base, we get a very interesting result! All the elements in the sequence have binary bits set to "1".

0.1111111 0.111111 0.11111 0.1111 0.111 0.11 0.1 0 1 11 111 1111 11111 111111 1111111
Required options
These options will be used automatically if you select this example.
Start generating powers of
two from this value.
Generate this many powers
of two.
Separate powers of two by this
symbol. (By default newline.)
Generate powers of two in
the positive direction.
For example: 2⁰, 2¹, 2², ...
For positive powers of two,
subtract one but for negative
add one. (Try in binary mode
to see the effect!)

### Pro tipsMaster online number tools

You can pass options to this tool using their codes as query arguments and it will automatically compute output. To get the code of an option, just hover over its icon. Here's how to type it in your browser's address bar. Click to try!

https://onlinetools.com/number/generate-powers-of-two?start=2&count=30&separator=%252C%20&increasing-sequence=true&plus-minus-one=false&decimal-base=true

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