# Convert -1 985 229 339 to a signed binary in two's complement representation, from a signed integer number in base 10 decimal system

## -1 985 229 339(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;
• 1 985 229 339 ÷ 2 = 992 614 669 + 1;
• 992 614 669 ÷ 2 = 496 307 334 + 1;
• 496 307 334 ÷ 2 = 248 153 667 + 0;
• 248 153 667 ÷ 2 = 124 076 833 + 1;
• 124 076 833 ÷ 2 = 62 038 416 + 1;
• 62 038 416 ÷ 2 = 31 019 208 + 0;
• 31 019 208 ÷ 2 = 15 509 604 + 0;
• 15 509 604 ÷ 2 = 7 754 802 + 0;
• 7 754 802 ÷ 2 = 3 877 401 + 0;
• 3 877 401 ÷ 2 = 1 938 700 + 1;
• 1 938 700 ÷ 2 = 969 350 + 0;
• 969 350 ÷ 2 = 484 675 + 0;
• 484 675 ÷ 2 = 242 337 + 1;
• 242 337 ÷ 2 = 121 168 + 1;
• 121 168 ÷ 2 = 60 584 + 0;
• 60 584 ÷ 2 = 30 292 + 0;
• 30 292 ÷ 2 = 15 146 + 0;
• 15 146 ÷ 2 = 7 573 + 0;
• 7 573 ÷ 2 = 3 786 + 1;
• 3 786 ÷ 2 = 1 893 + 0;
• 1 893 ÷ 2 = 946 + 1;
• 946 ÷ 2 = 473 + 0;
• 473 ÷ 2 = 236 + 1;
• 236 ÷ 2 = 118 + 0;
• 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 converted from decimal system to binary two's complement representation

 -1,985,229,339 to signed binary two's complement = ? Apr 14 11:48 UTC (GMT) 1,476 to signed binary two's complement = ? Apr 14 11:48 UTC (GMT) 10 to signed binary two's complement = ? Apr 14 11:48 UTC (GMT) 139,948,407,982,522 to signed binary two's complement = ? Apr 14 11:47 UTC (GMT) -2,100,261,239 to signed binary two's complement = ? Apr 14 11:47 UTC (GMT) 20 to signed binary two's complement = ? Apr 14 11:47 UTC (GMT) -342,529 to signed binary two's complement = ? Apr 14 11:47 UTC (GMT) -278 to signed binary two's complement = ? Apr 14 11:46 UTC (GMT) 100,111 to signed binary two's complement = ? Apr 14 11:46 UTC (GMT) 100,111 to signed binary two's complement = ? Apr 14 11:46 UTC (GMT) -2,865 to signed binary two's complement = ? Apr 14 11:46 UTC (GMT) 10 to signed binary two's complement = ? Apr 14 11:46 UTC (GMT) -342,558 to signed binary two's complement = ? Apr 14 11:45 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