# Signed: Integer -> Binary: 23 042 060 Convert the Integer Number to a Signed Binary. Converting and Writing the Base Ten Decimal System Signed Integer as Binary Code (Written in Base Two)

## Signed integer number 23 042 060_{(10)}

converted and written as a signed binary (base 2) = ?

### 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**; - 23 042 060 ÷ 2 = 11 521 030 +
**0**; - 11 521 030 ÷ 2 = 5 760 515 +
**0**; - 5 760 515 ÷ 2 = 2 880 257 +
**1**; - 2 880 257 ÷ 2 = 1 440 128 +
**1**; - 1 440 128 ÷ 2 = 720 064 +
**0**; - 720 064 ÷ 2 = 360 032 +
**0**; - 360 032 ÷ 2 = 180 016 +
**0**; - 180 016 ÷ 2 = 90 008 +
**0**; - 90 008 ÷ 2 = 45 004 +
**0**; - 45 004 ÷ 2 = 22 502 +
**0**; - 22 502 ÷ 2 = 11 251 +
**0**; - 11 251 ÷ 2 = 5 625 +
**1**; - 5 625 ÷ 2 = 2 812 +
**1**; - 2 812 ÷ 2 = 1 406 +
**0**; - 1 406 ÷ 2 = 703 +
**0**; - 703 ÷ 2 = 351 +
**1**; - 351 ÷ 2 = 175 +
**1**; - 175 ÷ 2 = 87 +
**1**; - 87 ÷ 2 = 43 +
**1**; - 43 ÷ 2 = 21 +
**1**; - 21 ÷ 2 = 10 +
**1**; - 10 ÷ 2 = 5 +
**0**; - 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.

#### 23 042 060_{(10)} = 1 0101 1111 1001 1000 0000 1100_{(2)}

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

#### The base 2 number's actual length, in bits: 25.

#### 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) is reserved for 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, 25,

#### 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 23 042 060_{(10)}, a signed integer number (with sign),

converted from decimal system (from base 10)

and written as a signed binary (in base 2):

## 23 042 060_{(10)} = 0000 0001 0101 1111 1001 1000 0000 1100

#### The first bit (the leftmost) is reserved for the sign:

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

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

## Convert signed integer numbers from the decimal system (base ten) to signed binary (written in base two)

### How to convert a base ten signed integer number to signed binary:

#### 1) Divide the positive version of the number repeatedly by 2, keeping track of each remainder. Stop when getting a quotient that is 0.

#### 2) Construct the base two representation by taking the previously calculated remainders starting from the last remainder up to the first one.

#### 3) Construct the positive binary computer representation so that the first bit is 0.

#### 4) Only if the initial number is negative, change the first bit (the leftmost), from 0 to 1. The leftmost bit is reserved for the sign, 1 = negative, 0 = positive.