Convert 256 from decimal to binary (base 2) notation:

Start by raising our base of 2 to a power starting at 0 and increasing by 1 until it is >= 256

2

2

2

2

2

2

2

2

2

Since 256 is equal to 256, we use our current power as our starting point which equals 8.

Now start building our binary notation working backwards from a power of 8.

We start with a total sum of 0:

2

The highest coefficient less than 1 we can multiply this by to stay under 256 is 1.

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

Adding our new value to our running total, we get: 0 + 256 = 256.

This = 256, so we assign our outside coefficient of 1 for this digit.

Our new sum becomes 256.

Our binary notation is now equal to 1

2

The highest coefficient less than 1 we can multiply this by to stay under 256 is 1.

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

Adding our new value to our running total, we get: 256 + 128 = 384.

This is > 256, so we assign a 0 for this digit.

Our total sum remains the same at 256.

Our binary notation is now equal to 10

2

The highest coefficient less than 1 we can multiply this by to stay under 256 is 1.

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

Adding our new value to our running total, we get: 256 + 64 = 320.

This is > 256, so we assign a 0 for this digit.

Our total sum remains the same at 256.

Our binary notation is now equal to 100

2

The highest coefficient less than 1 we can multiply this by to stay under 256 is 1.

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

Adding our new value to our running total, we get: 256 + 32 = 288.

This is > 256, so we assign a 0 for this digit.

Our total sum remains the same at 256.

Our binary notation is now equal to 1000

2

The highest coefficient less than 1 we can multiply this by to stay under 256 is 1.

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

Adding our new value to our running total, we get: 256 + 16 = 272.

This is > 256, so we assign a 0 for this digit.

Our total sum remains the same at 256.

Our binary notation is now equal to 10000

2

The highest coefficient less than 1 we can multiply this by to stay under 256 is 1.

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

Adding our new value to our running total, we get: 256 + 8 = 264.

This is > 256, so we assign a 0 for this digit.

Our total sum remains the same at 256.

Our binary notation is now equal to 100000

2

The highest coefficient less than 1 we can multiply this by to stay under 256 is 1.

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

Adding our new value to our running total, we get: 256 + 4 = 260.

This is > 256, so we assign a 0 for this digit.

Our total sum remains the same at 256.

Our binary notation is now equal to 1000000

2

The highest coefficient less than 1 we can multiply this by to stay under 256 is 1.

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

Adding our new value to our running total, we get: 256 + 2 = 258.

This is > 256, so we assign a 0 for this digit.

Our total sum remains the same at 256.

Our binary notation is now equal to 10000000

2

The highest coefficient less than 1 we can multiply this by to stay under 256 is 1.

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

Adding our new value to our running total, we get: 256 + 1 = 257.

This is > 256, so we assign a 0 for this digit.

Our total sum remains the same at 256.

Our binary notation is now equal to 100000000

We are done. 256 converted from decimal to binary notation equals