### 1. 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**; - 100 101 101 ÷ 2 = 50 050 550 +
**1**; - 50 050 550 ÷ 2 = 25 025 275 +
**0**; - 25 025 275 ÷ 2 = 12 512 637 +
**1**; - 12 512 637 ÷ 2 = 6 256 318 +
**1**; - 6 256 318 ÷ 2 = 3 128 159 +
**0**; - 3 128 159 ÷ 2 = 1 564 079 +
**1**; - 1 564 079 ÷ 2 = 782 039 +
**1**; - 782 039 ÷ 2 = 391 019 +
**1**; - 391 019 ÷ 2 = 195 509 +
**1**; - 195 509 ÷ 2 = 97 754 +
**1**; - 97 754 ÷ 2 = 48 877 +
**0**; - 48 877 ÷ 2 = 24 438 +
**1**; - 24 438 ÷ 2 = 12 219 +
**0**; - 12 219 ÷ 2 = 6 109 +
**1**; - 6 109 ÷ 2 = 3 054 +
**1**; - 3 054 ÷ 2 = 1 527 +
**0**; - 1 527 ÷ 2 = 763 +
**1**; - 763 ÷ 2 = 381 +
**1**; - 381 ÷ 2 = 190 +
**1**; - 190 ÷ 2 = 95 +
**0**; - 95 ÷ 2 = 47 +
**1**; - 47 ÷ 2 = 23 +
**1**; - 23 ÷ 2 = 11 +
**1**; - 11 ÷ 2 = 5 +
**1**; - 5 ÷ 2 = 2 +
**1**; - 2 ÷ 2 = 1 +
**0**; - 1 ÷ 2 = 0 +
**1**;

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

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

#### 100 101 101_{(10)} = 101 1111 0111 0110 1011 1110 1101_{(2)}

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

#### The base 2 number's actual length, in bits: 27.

#### 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, 27,

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

(we deal with a positive number at this moment)

#### === is: 32.

### 4. Get the positive binary computer representation on 32 bits (4 Bytes):

#### If needed, add extra 0s in front (to the left) of the base 2 number, up to the required length, 32.

## Number 100 101 101_{(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:

## 100 101 101_{(10)} = 0000 0101 1111 0111 0110 1011 1110 1101

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