### 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**; - 724 ÷ 2 = 362 +
**0**; - 362 ÷ 2 = 181 +
**0**; - 181 ÷ 2 = 90 +
**1**; - 90 ÷ 2 = 45 +
**0**; - 45 ÷ 2 = 22 +
**1**; - 22 ÷ 2 = 11 +
**0**; - 11 ÷ 2 = 5 +
**1**; - 5 ÷ 2 = 2 +
**1**; - 2 ÷ 2 = 1 +
**0**; - 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.

#### 724_{(10)} = 10 1101 0100_{(2)}

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

#### The base 2 number's actual length, in bits: 10.

#### 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; ...

#### The first bit (the leftmost) indicates the sign:

#### 0 = positive integer number, 1 = negative integer number

#### The least number that is:

#### 1) a power of 2

#### 2) and is larger than the actual length, 10,

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

(we deal with a positive number at this moment)

#### === is: 16.

### 5. Get the 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.

#### 724_{(10)} = 0000 0010 1101 0100

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

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

#### as a signed binary in one's complement representation,

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

### Reverse the digits, flip the digits:

#### Replace the bits set on 0 with 1s and the bits set on 1 with 0s.

#### -724_{(10)} = !(0000 0010 1101 0100)

## Number -724_{(10)}, a signed integer number (with sign), converted from decimal system (from base 10) and written as a signed binary in one's complement representation:

## -724_{(10)} = 1111 1101 0010 1011

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