## -27 581_{(10)} to a signed binary = ?

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

#### |-27 581| = 27 581

### 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**; - 27 581 ÷ 2 = 13 790 +
**1**; - 13 790 ÷ 2 = 6 895 +
**0**; - 6 895 ÷ 2 = 3 447 +
**1**; - 3 447 ÷ 2 = 1 723 +
**1**; - 1 723 ÷ 2 = 861 +
**1**; - 861 ÷ 2 = 430 +
**1**; - 430 ÷ 2 = 215 +
**0**; - 215 ÷ 2 = 107 +
**1**; - 107 ÷ 2 = 53 +
**1**; - 53 ÷ 2 = 26 +
**1**; - 26 ÷ 2 = 13 +
**0**; - 13 ÷ 2 = 6 +
**1**; - 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.

#### 27 581_{(10)} = 110 1011 1011 1101_{(2)}

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

#### The base 2 number's actual length, in bits: 15.

#### 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, 15,

#### 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:

#### 27 581_{(10)} = 0110 1011 1011 1101

### 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:

#### -27 581_{(10)} =

#### 1110 1011 1011 1101

## Number -27 581, a signed integer, converted from decimal system (base 10) to signed binary:

## -27 581_{(10)} = 1110 1011 1011 1101

#### 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