## How to convert the signed integer in decimal system (in base 10):

-6 256_{(10)}

to a signed binary

### 1. Start with the positive version of the number:

#### |-6 256| = 6 256

### 2. Divide the number repeatedly by 2:

#### Keep track of each remainder.

#### We stop when we get a quotient that is equal to zero.

- division = quotient +
**remainder**; - 6 256 ÷ 2 = 3 128 +
**0**; - 3 128 ÷ 2 = 1 564 +
**0**; - 1 564 ÷ 2 = 782 +
**0**; - 782 ÷ 2 = 391 +
**0**; - 391 ÷ 2 = 195 +
**1**; - 195 ÷ 2 = 97 +
**1**; - 97 ÷ 2 = 48 +
**1**; - 48 ÷ 2 = 24 +
**0**; - 24 ÷ 2 = 12 +
**0**; - 12 ÷ 2 = 6 +
**0**; - 6 ÷ 2 = 3 +
**0**; - 3 ÷ 2 = 1 +
**1**; - 1 ÷ 2 = 0 +
**1**;

### 3. Construct the base 2 representation of the positive number:

#### Take all the remainders starting from the bottom of the list constructed above.

#### 6 256_{(10)} = 1 1000 0111 0000_{(2)}

### 4. Determine the signed binary number bit length:

#### The base 2 number's actual length, in bits: 13.

#### A signed binary's bit length must be equal to a power of 2, as of:

2^{1} = 2; 2^{2} = 4; 2^{3} = 8; 2^{4} = 16; 2^{5} = 32; 2^{6} = 64; ...

#### First bit (the leftmost) is reserved for the sign:

0 = positive integer number, 1 = negative integer number

#### The least number that is:

#### a power of 2

#### and is larger than the actual length, 13,

#### so that the first bit (leftmost) could be zero

#### (we deal with a positive number at this moment)

#### is: 16.

### 5. Positive binary computer representation on 16 bits (2 Bytes):

#### If needed, add extra 0s in front (to the left) of the base 2 number, up to the required length, 16:

#### 6 256_{(10)} = 0001 1000 0111 0000

### 6. Get the negative integer number representation:

#### To get the negative integer number representation on 16 bits (2 Bytes),

#### change the first bit (the leftmost), from 0 to 1:

#### -6 256_{(10)} =

#### 1001 1000 0111 0000

## Conclusion:

## Number -6 256, a signed integer, converted from decimal system (base 10) to signed binary:

## -6 256_{(10)} = 1001 1000 0111 0000

#### First bit (the leftmost) is reserved for the sign:

0 = positive integer number, 1 = negative integer number

#### Spaces used to group digits: for binary, by 4; for decimal, by 3.

### More operations of this kind:

## Convert signed integer numbers from the decimal system (base ten) to signed binary