## -9 533 052_{(10)} to a signed binary one's complement representation = ?

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

#### |-9 533 052| = 9 533 052

### 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**; - 9 533 052 ÷ 2 = 4 766 526 +
**0**; - 4 766 526 ÷ 2 = 2 383 263 +
**0**; - 2 383 263 ÷ 2 = 1 191 631 +
**1**; - 1 191 631 ÷ 2 = 595 815 +
**1**; - 595 815 ÷ 2 = 297 907 +
**1**; - 297 907 ÷ 2 = 148 953 +
**1**; - 148 953 ÷ 2 = 74 476 +
**1**; - 74 476 ÷ 2 = 37 238 +
**0**; - 37 238 ÷ 2 = 18 619 +
**0**; - 18 619 ÷ 2 = 9 309 +
**1**; - 9 309 ÷ 2 = 4 654 +
**1**; - 4 654 ÷ 2 = 2 327 +
**0**; - 2 327 ÷ 2 = 1 163 +
**1**; - 1 163 ÷ 2 = 581 +
**1**; - 581 ÷ 2 = 290 +
**1**; - 290 ÷ 2 = 145 +
**0**; - 145 ÷ 2 = 72 +
**1**; - 72 ÷ 2 = 36 +
**0**; - 36 ÷ 2 = 18 +
**0**; - 18 ÷ 2 = 9 +
**0**; - 9 ÷ 2 = 4 +
**1**; - 4 ÷ 2 = 2 +
**0**; - 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.

#### 9 533 052_{(10)} = 1001 0001 0111 0110 0111 1100_{(2)}

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

#### The base 2 number's actual length, in bits: 24.

#### 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, 24,

#### 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:

#### 9 533 052_{(10)} = 0000 0000 1001 0001 0111 0110 0111 1100

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

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

#### !(0000 0000 1001 0001 0111 0110 0111 1100) =

#### 1111 1111 0110 1110 1000 1001 1000 0011

## Number -9 533 052, a signed integer, converted from decimal system (base 10) to a signed binary one's complement representation:

## -9 533 052_{(10)} = 1111 1111 0110 1110 1000 1001 1000 0011

#### 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