Convert -183 761 713 803 299 to a Signed Binary in One's (1's) Complement Representation

How to convert decimal number -183 761 713 803 299(10) to a signed binary in one's (1's) complement representation

What are the steps to convert decimal number
-183 761 713 803 299 to a signed binary in one's (1's) complement representation?

  • A signed integer, written in base ten, or a decimal system number, is a number written using the digits 0 through 9 and the sign, which can be positive (+) or negative (-). If positive, the sign is usually not written. A number written in base two, or binary, is a number written using only the digits 0 and 1.

1. Start with the positive version of the number:

|-183 761 713 803 299| = 183 761 713 803 299

2. Divide the number repeatedly by 2:

Keep track of each remainder.

Stop when you get a quotient that is equal to zero.


  • division = quotient + remainder;
  • 183 761 713 803 299 ÷ 2 = 91 880 856 901 649 + 1;
  • 91 880 856 901 649 ÷ 2 = 45 940 428 450 824 + 1;
  • 45 940 428 450 824 ÷ 2 = 22 970 214 225 412 + 0;
  • 22 970 214 225 412 ÷ 2 = 11 485 107 112 706 + 0;
  • 11 485 107 112 706 ÷ 2 = 5 742 553 556 353 + 0;
  • 5 742 553 556 353 ÷ 2 = 2 871 276 778 176 + 1;
  • 2 871 276 778 176 ÷ 2 = 1 435 638 389 088 + 0;
  • 1 435 638 389 088 ÷ 2 = 717 819 194 544 + 0;
  • 717 819 194 544 ÷ 2 = 358 909 597 272 + 0;
  • 358 909 597 272 ÷ 2 = 179 454 798 636 + 0;
  • 179 454 798 636 ÷ 2 = 89 727 399 318 + 0;
  • 89 727 399 318 ÷ 2 = 44 863 699 659 + 0;
  • 44 863 699 659 ÷ 2 = 22 431 849 829 + 1;
  • 22 431 849 829 ÷ 2 = 11 215 924 914 + 1;
  • 11 215 924 914 ÷ 2 = 5 607 962 457 + 0;
  • 5 607 962 457 ÷ 2 = 2 803 981 228 + 1;
  • 2 803 981 228 ÷ 2 = 1 401 990 614 + 0;
  • 1 401 990 614 ÷ 2 = 700 995 307 + 0;
  • 700 995 307 ÷ 2 = 350 497 653 + 1;
  • 350 497 653 ÷ 2 = 175 248 826 + 1;
  • 175 248 826 ÷ 2 = 87 624 413 + 0;
  • 87 624 413 ÷ 2 = 43 812 206 + 1;
  • 43 812 206 ÷ 2 = 21 906 103 + 0;
  • 21 906 103 ÷ 2 = 10 953 051 + 1;
  • 10 953 051 ÷ 2 = 5 476 525 + 1;
  • 5 476 525 ÷ 2 = 2 738 262 + 1;
  • 2 738 262 ÷ 2 = 1 369 131 + 0;
  • 1 369 131 ÷ 2 = 684 565 + 1;
  • 684 565 ÷ 2 = 342 282 + 1;
  • 342 282 ÷ 2 = 171 141 + 0;
  • 171 141 ÷ 2 = 85 570 + 1;
  • 85 570 ÷ 2 = 42 785 + 0;
  • 42 785 ÷ 2 = 21 392 + 1;
  • 21 392 ÷ 2 = 10 696 + 0;
  • 10 696 ÷ 2 = 5 348 + 0;
  • 5 348 ÷ 2 = 2 674 + 0;
  • 2 674 ÷ 2 = 1 337 + 0;
  • 1 337 ÷ 2 = 668 + 1;
  • 668 ÷ 2 = 334 + 0;
  • 334 ÷ 2 = 167 + 0;
  • 167 ÷ 2 = 83 + 1;
  • 83 ÷ 2 = 41 + 1;
  • 41 ÷ 2 = 20 + 1;
  • 20 ÷ 2 = 10 + 0;
  • 10 ÷ 2 = 5 + 0;
  • 5 ÷ 2 = 2 + 1;
  • 2 ÷ 2 = 1 + 0;
  • 1 ÷ 2 = 0 + 1;

3. Construct the base 2 representation of the positive number:

Take all the remainders starting from the bottom of the list constructed above.

183 761 713 803 299(10) = 1010 0111 0010 0001 0101 1011 1010 1100 1011 0000 0010 0011(2)

4. Determine the signed binary number bit length:

  • The base 2 number's actual length, in bits: 48.

  • A signed binary's bit length must be equal to a power of 2, as of:
  • 21 = 2; 22 = 4; 23 = 8; 24 = 16; 25 = 32; 26 = 64; ...
  • The first bit (the leftmost) indicates the sign:
  • 0 = positive integer number, 1 = negative integer number

The least number that is:

1) a power of 2

2) and is larger than the actual length, 48,

3) so that the first bit (leftmost) could be zero
(we deal with a positive number at this moment)

=== is: 64.


5. Get the positive binary computer representation on 64 bits (8 Bytes):

If needed, add extra 0s in front (to the left) of the base 2 number, up to the required length, 64.


183 761 713 803 299(10) = 0000 0000 0000 0000 1010 0111 0010 0001 0101 1011 1010 1100 1011 0000 0010 0011

6. Get the negative integer number representation:

  • To write the negative integer number on 64 bits (8 Bytes), as a signed binary in one's complement representation,

  • ... Reverse all the bits from 0 to 1 and from 1 to 0 (flip the digits).


-183 761 713 803 299(10) = !(0000 0000 0000 0000 1010 0111 0010 0001 0101 1011 1010 1100 1011 0000 0010 0011)


Decimal Number -183 761 713 803 299(10) converted to signed binary in one's complement representation:

-183 761 713 803 299(10) = 1111 1111 1111 1111 0101 1000 1101 1110 1010 0100 0101 0011 0100 1111 1101 1100

Spaces were used to group digits: for binary, by 4, for decimal, by 3.

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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
  • Number -49(10), signed integer, converted from the decimal system (base 10) to signed binary in one's complement representation = 1100 1110