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Convert 4004 from decimal to binary

(base 2) notation:

Power Test

Raise our base of 2 to a power

Start at 0 and increasing by 1 until it is >= 4004

20 = 1

21 = 2

22 = 4

23 = 8

24 = 16

25 = 32

26 = 64

27 = 128

28 = 256

29 = 512

210 = 1024

211 = 2048

212 = 4096 <--- Stop: This is greater than 4004

Since 4096 is greater than 4004, we use 1 power less as our starting point which equals 11

Build binary notation

Work backwards from a power of 11

We start with a total sum of 0:

211 = 2048

The highest coefficient less than 1 we can multiply this by to stay under 4004 is 1

Multiplying this coefficient by our original value, we get: 1 * 2048 = 2048

Add our new value to our running total, we get:
0 + 2048 = 2048

This is <= 4004, so we assign our outside coefficient of 1 for this digit.

Our new sum becomes 2048

Our binary notation is now equal to 1

210 = 1024

The highest coefficient less than 1 we can multiply this by to stay under 4004 is 1

Multiplying this coefficient by our original value, we get: 1 * 1024 = 1024

Add our new value to our running total, we get:
2048 + 1024 = 3072

This is <= 4004, so we assign our outside coefficient of 1 for this digit.

Our new sum becomes 3072

Our binary notation is now equal to 11

29 = 512

The highest coefficient less than 1 we can multiply this by to stay under 4004 is 1

Multiplying this coefficient by our original value, we get: 1 * 512 = 512

Add our new value to our running total, we get:
3072 + 512 = 3584

This is <= 4004, so we assign our outside coefficient of 1 for this digit.

Our new sum becomes 3584

Our binary notation is now equal to 111

28 = 256

The highest coefficient less than 1 we can multiply this by to stay under 4004 is 1

Multiplying this coefficient by our original value, we get: 1 * 256 = 256

Add our new value to our running total, we get:
3584 + 256 = 3840

This is <= 4004, so we assign our outside coefficient of 1 for this digit.

Our new sum becomes 3840

Our binary notation is now equal to 1111

27 = 128

The highest coefficient less than 1 we can multiply this by to stay under 4004 is 1

Multiplying this coefficient by our original value, we get: 1 * 128 = 128

Add our new value to our running total, we get:
3840 + 128 = 3968

This is <= 4004, so we assign our outside coefficient of 1 for this digit.

Our new sum becomes 3968

Our binary notation is now equal to 11111

26 = 64

The highest coefficient less than 1 we can multiply this by to stay under 4004 is 1

Multiplying this coefficient by our original value, we get: 1 * 64 = 64

Add our new value to our running total, we get:
3968 + 64 = 4032

This is > 4004, so we assign a 0 for this digit.

Our total sum remains the same at 3968

Our binary notation is now equal to 111110

25 = 32

The highest coefficient less than 1 we can multiply this by to stay under 4004 is 1

Multiplying this coefficient by our original value, we get: 1 * 32 = 32

Add our new value to our running total, we get:
3968 + 32 = 4000

This is <= 4004, so we assign our outside coefficient of 1 for this digit.

Our new sum becomes 4000

Our binary notation is now equal to 1111101

24 = 16

The highest coefficient less than 1 we can multiply this by to stay under 4004 is 1

Multiplying this coefficient by our original value, we get: 1 * 16 = 16

Add our new value to our running total, we get:
4000 + 16 = 4016

This is > 4004, so we assign a 0 for this digit.

Our total sum remains the same at 4000

Our binary notation is now equal to 11111010

23 = 8

The highest coefficient less than 1 we can multiply this by to stay under 4004 is 1

Multiplying this coefficient by our original value, we get: 1 * 8 = 8

Add our new value to our running total, we get:
4000 + 8 = 4008

This is > 4004, so we assign a 0 for this digit.

Our total sum remains the same at 4000

Our binary notation is now equal to 111110100

22 = 4

The highest coefficient less than 1 we can multiply this by to stay under 4004 is 1

Multiplying this coefficient by our original value, we get: 1 * 4 = 4

Add our new value to our running total, we get:
4000 + 4 = 4004

This = 4004, so we assign our outside coefficient of 1 for this digit.

Our new sum becomes 4004

Our binary notation is now equal to 1111101001

21 = 2

The highest coefficient less than 1 we can multiply this by to stay under 4004 is 1

Multiplying this coefficient by our original value, we get: 1 * 2 = 2

Add our new value to our running total, we get:
4004 + 2 = 4006

This is > 4004, so we assign a 0 for this digit.

Our total sum remains the same at 4004

Our binary notation is now equal to 11111010010

20 = 1

The highest coefficient less than 1 we can multiply this by to stay under 4004 is 1

Multiplying this coefficient by our original value, we get: 1 * 1 = 1

Add our new value to our running total, we get:
4004 + 1 = 4005

This is > 4004, so we assign a 0 for this digit.

Our total sum remains the same at 4004

Our binary notation is now equal to 111110100100

Final Answer

We are done. 4004 converted from decimal to binary notation equals 1111101001002.

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What is the Answer?

We are done. 4004 converted from decimal to binary notation equals 1111101001002.

How does the Base Change Conversions Calculator work?

Free Base Change Conversions Calculator - Converts a positive integer to Binary-Octal-Hexadecimal Notation or Binary-Octal-Hexadecimal Notation to a positive integer. Also converts any positive integer in base 10 to another positive integer base (Change Base Rule or Base Change Rule or Base Conversion)
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