## How to convert the signed integer in decimal system (in base 10):

-1 840 012 358_{(10)}

to a signed binary

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

#### |-1 840 012 358| = 1 840 012 358

### 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**; - 1 840 012 358 ÷ 2 = 920 006 179 +
**0**; - 920 006 179 ÷ 2 = 460 003 089 +
**1**; - 460 003 089 ÷ 2 = 230 001 544 +
**1**; - 230 001 544 ÷ 2 = 115 000 772 +
**0**; - 115 000 772 ÷ 2 = 57 500 386 +
**0**; - 57 500 386 ÷ 2 = 28 750 193 +
**0**; - 28 750 193 ÷ 2 = 14 375 096 +
**1**; - 14 375 096 ÷ 2 = 7 187 548 +
**0**; - 7 187 548 ÷ 2 = 3 593 774 +
**0**; - 3 593 774 ÷ 2 = 1 796 887 +
**0**; - 1 796 887 ÷ 2 = 898 443 +
**1**; - 898 443 ÷ 2 = 449 221 +
**1**; - 449 221 ÷ 2 = 224 610 +
**1**; - 224 610 ÷ 2 = 112 305 +
**0**; - 112 305 ÷ 2 = 56 152 +
**1**; - 56 152 ÷ 2 = 28 076 +
**0**; - 28 076 ÷ 2 = 14 038 +
**0**; - 14 038 ÷ 2 = 7 019 +
**0**; - 7 019 ÷ 2 = 3 509 +
**1**; - 3 509 ÷ 2 = 1 754 +
**1**; - 1 754 ÷ 2 = 877 +
**0**; - 877 ÷ 2 = 438 +
**1**; - 438 ÷ 2 = 219 +
**0**; - 219 ÷ 2 = 109 +
**1**; - 109 ÷ 2 = 54 +
**1**; - 54 ÷ 2 = 27 +
**0**; - 27 ÷ 2 = 13 +
**1**; - 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.

#### 1 840 012 358_{(10)} = 110 1101 1010 1100 0101 1100 0100 0110_{(2)}

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

#### The base 2 number's actual length, in bits: 31.

#### 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, 31,

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

#### (we deal with a positive number at this moment)

#### is: 32.

### 5. 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:

#### 1 840 012 358_{(10)} = 0110 1101 1010 1100 0101 1100 0100 0110

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

#### To get the negative integer number representation on 32 bits (4 Bytes),

#### change the first bit (the leftmost), from 0 to 1:

#### -1 840 012 358_{(10)} =

#### 1110 1101 1010 1100 0101 1100 0100 0110

## Conclusion:

## Number -1 840 012 358, a signed integer, converted from decimal system (base 10) to signed binary:

## -1 840 012 358_{(10)} = 1110 1101 1010 1100 0101 1100 0100 0110

#### 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