# Base ten decimal system signed integer number -1 112 426 078 converted to signed binary in one's complement representation

## How to convert a signed integer in decimal system (in base 10): -1 112 426 078(10) to a signed binary one's complement representation

### 2. Divide the number repeatedly by 2, keeping track of each remainder, until we get a quotient that is equal to zero:

• division = quotient + remainder;
• 1 112 426 078 ÷ 2 = 556 213 039 + 0;
• 556 213 039 ÷ 2 = 278 106 519 + 1;
• 278 106 519 ÷ 2 = 139 053 259 + 1;
• 139 053 259 ÷ 2 = 69 526 629 + 1;
• 69 526 629 ÷ 2 = 34 763 314 + 1;
• 34 763 314 ÷ 2 = 17 381 657 + 0;
• 17 381 657 ÷ 2 = 8 690 828 + 1;
• 8 690 828 ÷ 2 = 4 345 414 + 0;
• 4 345 414 ÷ 2 = 2 172 707 + 0;
• 2 172 707 ÷ 2 = 1 086 353 + 1;
• 1 086 353 ÷ 2 = 543 176 + 1;
• 543 176 ÷ 2 = 271 588 + 0;
• 271 588 ÷ 2 = 135 794 + 0;
• 135 794 ÷ 2 = 67 897 + 0;
• 67 897 ÷ 2 = 33 948 + 1;
• 33 948 ÷ 2 = 16 974 + 0;
• 16 974 ÷ 2 = 8 487 + 0;
• 8 487 ÷ 2 = 4 243 + 1;
• 4 243 ÷ 2 = 2 121 + 1;
• 2 121 ÷ 2 = 1 060 + 1;
• 1 060 ÷ 2 = 530 + 0;
• 530 ÷ 2 = 265 + 0;
• 265 ÷ 2 = 132 + 1;
• 132 ÷ 2 = 66 + 0;
• 66 ÷ 2 = 33 + 0;
• 33 ÷ 2 = 16 + 1;
• 16 ÷ 2 = 8 + 0;
• 8 ÷ 2 = 4 + 0;
• 4 ÷ 2 = 2 + 0;
• 2 ÷ 2 = 1 + 0;
• 1 ÷ 2 = 0 + 1;

## Latest signed integers numbers converted from decimal system to signed binary in one's complement representation

 -1,112,426,078 = 1011 1101 1011 0001 1011 1001 1010 0001 Dec 06 18:52 UTC (GMT) 101,100 = 0000 0000 0000 0001 1000 1010 1110 1100 Dec 06 18:50 UTC (GMT) 666 = 0000 0010 1001 1010 Dec 06 18:49 UTC (GMT) 110,111,000 = 0000 0110 1001 0000 0010 1001 0001 1000 Dec 06 18:49 UTC (GMT) 10,010,100 = 0000 0000 1001 1000 1011 1101 1111 0100 Dec 06 18:48 UTC (GMT) -146 = 1111 1111 0110 1101 Dec 06 18:48 UTC (GMT) 512 = 0000 0010 0000 0000 Dec 06 18:46 UTC (GMT) 110,111,011,101 = 0000 0000 0000 0000 0000 0000 0001 1001 1010 0011 0010 0000 1011 0001 0001 1101 Dec 06 18:46 UTC (GMT) -522,962 = 1111 1111 1111 1000 0000 0101 0010 1101 Dec 06 18:43 UTC (GMT) -9,387 = 1101 1011 0101 0100 Dec 06 18:41 UTC (GMT) 44 = 0010 1100 Dec 06 18:40 UTC (GMT) -89 = 1010 0110 Dec 06 18:39 UTC (GMT) 2,147,483,647 = 0111 1111 1111 1111 1111 1111 1111 1111 Dec 06 18:36 UTC (GMT) All decimal integer numbers converted to signed binary one's complement representation

## How to convert signed integers from the decimal system to signed binary in one's complement representation

### Follow the steps below to convert a signed base 10 integer number to signed binary in one's complement representation:

• 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.

### Example: convert the negative number -49 from the decimal system (base ten) to signed binary one's complement:

• 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
• 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