### 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**; - 10 111 110 151 ÷ 2 = 5 055 555 075 +
**1**; - 5 055 555 075 ÷ 2 = 2 527 777 537 +
**1**; - 2 527 777 537 ÷ 2 = 1 263 888 768 +
**1**; - 1 263 888 768 ÷ 2 = 631 944 384 +
**0**; - 631 944 384 ÷ 2 = 315 972 192 +
**0**; - 315 972 192 ÷ 2 = 157 986 096 +
**0**; - 157 986 096 ÷ 2 = 78 993 048 +
**0**; - 78 993 048 ÷ 2 = 39 496 524 +
**0**; - 39 496 524 ÷ 2 = 19 748 262 +
**0**; - 19 748 262 ÷ 2 = 9 874 131 +
**0**; - 9 874 131 ÷ 2 = 4 937 065 +
**1**; - 4 937 065 ÷ 2 = 2 468 532 +
**1**; - 2 468 532 ÷ 2 = 1 234 266 +
**0**; - 1 234 266 ÷ 2 = 617 133 +
**0**; - 617 133 ÷ 2 = 308 566 +
**1**; - 308 566 ÷ 2 = 154 283 +
**0**; - 154 283 ÷ 2 = 77 141 +
**1**; - 77 141 ÷ 2 = 38 570 +
**1**; - 38 570 ÷ 2 = 19 285 +
**0**; - 19 285 ÷ 2 = 9 642 +
**1**; - 9 642 ÷ 2 = 4 821 +
**0**; - 4 821 ÷ 2 = 2 410 +
**1**; - 2 410 ÷ 2 = 1 205 +
**0**; - 1 205 ÷ 2 = 602 +
**1**; - 602 ÷ 2 = 301 +
**0**; - 301 ÷ 2 = 150 +
**1**; - 150 ÷ 2 = 75 +
**0**; - 75 ÷ 2 = 37 +
**1**; - 37 ÷ 2 = 18 +
**1**; - 18 ÷ 2 = 9 +
**0**; - 9 ÷ 2 = 4 +
**1**; - 4 ÷ 2 = 2 +
**0**; - 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.

#### 10 111 110 151_{(10)} = 10 0101 1010 1010 1011 0100 1100 0000 0111_{(2)}

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

#### The base 2 number's actual length, in bits: 34.

#### 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, 34,

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

(we deal with a positive number at this moment)

#### === is: 64.

### 4. Get the positive binary computer representation on 64 bits (8 Bytes):

#### If needed, add extra 0s in front (to the left) of the base 2 number, up to the required length, 64.

## Number 10 111 110 151_{(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:

## 10 111 110 151_{(10)} = 0000 0000 0000 0000 0000 0000 0000 0010 0101 1010 1010 1011 0100 1100 0000 0111

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