# Convert -119 999 999 995 to a signed binary in two's complement representation, from a signed integer number in base 10 decimal system

## -119 999 999 995(10) to a signed binary two's complement representation = ?

### 2. Divide the number repeatedly by 2:

#### We stop when we get a quotient that is equal to zero.

• division = quotient + remainder;
• 119 999 999 995 ÷ 2 = 59 999 999 997 + 1;
• 59 999 999 997 ÷ 2 = 29 999 999 998 + 1;
• 29 999 999 998 ÷ 2 = 14 999 999 999 + 0;
• 14 999 999 999 ÷ 2 = 7 499 999 999 + 1;
• 7 499 999 999 ÷ 2 = 3 749 999 999 + 1;
• 3 749 999 999 ÷ 2 = 1 874 999 999 + 1;
• 1 874 999 999 ÷ 2 = 937 499 999 + 1;
• 937 499 999 ÷ 2 = 468 749 999 + 1;
• 468 749 999 ÷ 2 = 234 374 999 + 1;
• 234 374 999 ÷ 2 = 117 187 499 + 1;
• 117 187 499 ÷ 2 = 58 593 749 + 1;
• 58 593 749 ÷ 2 = 29 296 874 + 1;
• 29 296 874 ÷ 2 = 14 648 437 + 0;
• 14 648 437 ÷ 2 = 7 324 218 + 1;
• 7 324 218 ÷ 2 = 3 662 109 + 0;
• 3 662 109 ÷ 2 = 1 831 054 + 1;
• 1 831 054 ÷ 2 = 915 527 + 0;
• 915 527 ÷ 2 = 457 763 + 1;
• 457 763 ÷ 2 = 228 881 + 1;
• 228 881 ÷ 2 = 114 440 + 1;
• 114 440 ÷ 2 = 57 220 + 0;
• 57 220 ÷ 2 = 28 610 + 0;
• 28 610 ÷ 2 = 14 305 + 0;
• 14 305 ÷ 2 = 7 152 + 1;
• 7 152 ÷ 2 = 3 576 + 0;
• 3 576 ÷ 2 = 1 788 + 0;
• 1 788 ÷ 2 = 894 + 0;
• 894 ÷ 2 = 447 + 0;
• 447 ÷ 2 = 223 + 1;
• 223 ÷ 2 = 111 + 1;
• 111 ÷ 2 = 55 + 1;
• 55 ÷ 2 = 27 + 1;
• 27 ÷ 2 = 13 + 1;
• 13 ÷ 2 = 6 + 1;
• 6 ÷ 2 = 3 + 0;
• 3 ÷ 2 = 1 + 1;
• 1 ÷ 2 = 0 + 1;

## Latest signed integers converted from decimal system to binary two's complement representation

 -119,999,999,995 to signed binary two's complement = ? Jun 13 23:55 UTC (GMT) 1,001,000,102 to signed binary two's complement = ? Jun 13 23:55 UTC (GMT) -2,705 to signed binary two's complement = ? Jun 13 23:55 UTC (GMT) -1,326,191,591 to signed binary two's complement = ? Jun 13 23:54 UTC (GMT) -1,082,130,435 to signed binary two's complement = ? Jun 13 23:54 UTC (GMT) 34,909 to signed binary two's complement = ? Jun 13 23:54 UTC (GMT) -15,367 to signed binary two's complement = ? Jun 13 23:54 UTC (GMT) -28,665 to signed binary two's complement = ? Jun 13 23:54 UTC (GMT) 3,584 to signed binary two's complement = ? Jun 13 23:53 UTC (GMT) 123,138 to signed binary two's complement = ? Jun 13 23:53 UTC (GMT) 23,179 to signed binary two's complement = ? Jun 13 23:53 UTC (GMT) 20,002,003 to signed binary two's complement = ? Jun 13 23:52 UTC (GMT) 178 to signed binary two's complement = ? Jun 13 23:52 UTC (GMT) All decimal integer numbers converted to signed binary two's complement representation

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

### Follow the steps below to convert a signed base 10 integer number to signed binary in two'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, keeping track of each remainder, until we get a quotient that is 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, add extra bits on 0 in front (to the left) of the base 2 number above, up to the required length, so that the first bit (the leftmost) will 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 1s and all 1 bits with 0s (reversing the digits).
• 6. To get the negative integer number, in signed binary two's complement representation, add 1 to the number above.

### Example: convert the negative number -60 from the decimal system (base ten) to signed binary in two's complement:

• 1. Start with the positive version of the number: |-60| = 60
• 2. Divide repeatedly 60 by 2, keeping track of each remainder:
• division = quotient + remainder
• 60 ÷ 2 = 30 + 0
• 30 ÷ 2 = 15 + 0
• 15 ÷ 2 = 7 + 1
• 7 ÷ 2 = 3 + 1
• 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:
60(10) = 11 1100(2)
• 4. Bit length of base 2 representation number is 6, so the positive binary computer representation of a signed binary will take in this particular case 8 bits (the least power of 2 larger than 6) - add extra 0 digits in front of the base 2 number, up to the required length:
60(10) = 0011 1100(2)
• 5. To get the negative integer number representation in signed binary one's complement, replace all the 0 bits with 1s and all 1 bits with 0s (reversing the digits):
!(0011 1100) = 1100 0011
• 6. To get the negative integer number, signed binary in two's complement representation, add 1 to the number above:
-60(10) = 1100 0011 + 1 = 1100 0100