- division = quotient +
**remainder**; - 84 742 ÷ 2 = 42 371 +
**0**; - 42 371 ÷ 2 = 21 185 +
**1**; - 21 185 ÷ 2 = 10 592 +
**1**; - 10 592 ÷ 2 = 5 296 +
**0**; - 5 296 ÷ 2 = 2 648 +
**0**; - 2 648 ÷ 2 = 1 324 +
**0**; - 1 324 ÷ 2 = 662 +
**0**; - 662 ÷ 2 = 331 +
**0**; - 331 ÷ 2 = 165 +
**1**; - 165 ÷ 2 = 82 +
**1**; - 82 ÷ 2 = 41 +
**0**; - 41 ÷ 2 = 20 +
**1**; - 20 ÷ 2 = 10 +
**0**; - 10 ÷ 2 = 5 +
**0**; - 5 ÷ 2 = 2 +
**1**; - 2 ÷ 2 = 1 +
**0**; - 1 ÷ 2 = 0 +
**1**;

(we deal with a positive number at this moment)

- 1. If the number to be converted is negative, start with the positive version of the number.
- 2. Divide repeatedly by 2 the positive representation of the integer number that is to be converted to binary, keeping track of each remainder, until we get a quotient that is equal to ZERO.
- 3. Construct the base 2 representation of the positive number, by taking all the remainders starting from the bottom of the list constructed above. Thus, the last remainder of the divisions becomes the first symbol (the leftmost) of the base two number, while the first remainder becomes the last symbol (the rightmost).
- 4. Binary numbers represented in computer language must have 4, 8, 16, 32, 64, ... bit length (a power of 2) - if needed, fill in '0' bits in front (to the left) of the base 2 number calculated above, up to the right length; this way the first bit (leftmost) will always be '0', correctly representing a positive number.
- 5. To get the negative integer number representation in signed binary one's complement, replace all '0' bits with '1's and all '1' bits with '0's.

- 1. Start with the positive version of the number: |-49| = 49
- 2. Divide repeatedly 49 by 2, keeping track of each remainder:
- division = quotient +
**remainder** - 49 ÷ 2 = 24 +
**1** - 24 ÷ 2 = 12 +
**0** - 12 ÷ 2 = 6 +
**0** - 6 ÷ 2 = 3 +
**0** - 3 ÷ 2 = 1 +
**1** - 1 ÷ 2 = 0 +
**1**

- division = quotient +
- 3. Construct the base 2 representation of the positive number, by taking all the remainders starting from the bottom of the list constructed above:

49_{(10)}= 11 0001_{(2)} - 4. The actual bit length of base 2 representation is 6, so the positive binary computer representation of a signed binary will take in this case 8 bits (the least power of 2 that is larger than 6) - add '0's in front of the base 2 number, up to the required length:

49_{(10)}= 0011 0001_{(2)} - 5. To get the negative integer number representation in signed binary one's complement, replace all '0' bits with '1's and all '1' bits with '0's:

-49_{(10)}= 1100 1110

### 1.1. Unsigned integer -> Unsigned binary

### 1.2. Signed integer -> Signed binary

### 1.3. Signed integer -> Signed binary one's complement

### 1.4. Signed integer -> Signed binary two's complement

### 2.1. Decimal -> 32bit single precision IEEE 754 binary floating point

### 2.2. Decimal -> 64bit double precision IEEE 754 binary floating point

### 3.1. Unsigned binary -> Unsigned integer

### 3.2. Signed binary -> Signed integer

### 3.3. Signed binary one's complement -> Signed integer

### 3.4. Signed binary two's complement -> Signed integer