## -13 322_{(10)} to a signed binary one's complement representation = ?

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

#### |-13 322| = 13 322

### 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**; - 13 322 ÷ 2 = 6 661 +
**0**; - 6 661 ÷ 2 = 3 330 +
**1**; - 3 330 ÷ 2 = 1 665 +
**0**; - 1 665 ÷ 2 = 832 +
**1**; - 832 ÷ 2 = 416 +
**0**; - 416 ÷ 2 = 208 +
**0**; - 208 ÷ 2 = 104 +
**0**; - 104 ÷ 2 = 52 +
**0**; - 52 ÷ 2 = 26 +
**0**; - 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.

#### 13 322_{(10)} = 11 0100 0000 1010_{(2)}

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

#### The base 2 number's actual length, in bits: 14.

#### 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) indicates the sign,

1 = negative, 0 = positive.

#### The least number that is:

#### a power of 2

#### and is larger than the actual length, 14,

#### 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:

#### 13 322_{(10)} = 0011 0100 0000 1010

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

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

#### signed binary one's complement,

#### replace all the bits on 0 with 1s

#### and all the bits set on 1 with 0s

#### (reverse the digits, flip the digits)

#### !(0011 0100 0000 1010) =

#### 1100 1011 1111 0101

## Number -13 322, a signed integer, converted from decimal system (base 10) to a signed binary one's complement representation:

## -13 322_{(10)} = 1100 1011 1111 0101

#### 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 one's complement representation