# Base ten decimal system signed integer number 15 213 converted to signed binary in one's complement representation

## How to convert a signed integer in decimal system (in base 10): 15 213(10) to a signed binary one's complement representation

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

• division = quotient + remainder;
• 15 213 ÷ 2 = 7 606 + 1;
• 7 606 ÷ 2 = 3 803 + 0;
• 3 803 ÷ 2 = 1 901 + 1;
• 1 901 ÷ 2 = 950 + 1;
• 950 ÷ 2 = 475 + 0;
• 475 ÷ 2 = 237 + 1;
• 237 ÷ 2 = 118 + 1;
• 118 ÷ 2 = 59 + 0;
• 59 ÷ 2 = 29 + 1;
• 29 ÷ 2 = 14 + 1;
• 14 ÷ 2 = 7 + 0;
• 7 ÷ 2 = 3 + 1;
• 3 ÷ 2 = 1 + 1;
• 1 ÷ 2 = 0 + 1;

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

 15,213 = 0011 1011 0110 1101 Feb 18 21:40 UTC (GMT) 158 = 0000 0000 1001 1110 Feb 18 21:39 UTC (GMT) -57 = 1100 0110 Feb 18 21:37 UTC (GMT) -167 = 1111 1111 0101 1000 Feb 18 21:34 UTC (GMT) 140 = 0000 0000 1000 1100 Feb 18 21:32 UTC (GMT) 821 = 0000 0011 0011 0101 Feb 18 21:29 UTC (GMT) 11,121,604 = 0000 0000 1010 1001 1011 0011 1100 0100 Feb 18 21:28 UTC (GMT) 14,752 = 0011 1001 1010 0000 Feb 18 21:24 UTC (GMT) -83 = 1010 1100 Feb 18 21:19 UTC (GMT) 25,610 = 0110 0100 0000 1010 Feb 18 21:17 UTC (GMT) 111,000 = 0000 0000 0000 0001 1011 0001 1001 1000 Feb 18 21:13 UTC (GMT) -1,980 = 1111 1000 0100 0011 Feb 18 21:10 UTC (GMT) 111,010 = 0000 0000 0000 0001 1011 0001 1010 0010 Feb 18 21:06 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