Convert -8 739 296 668 918 793 681 to a Signed Binary in One's (1's) Complement Representation

How to convert decimal number -8 739 296 668 918 793 681(10) to a signed binary in one's (1's) complement representation

What are the steps to convert decimal number
-8 739 296 668 918 793 681 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:

|-8 739 296 668 918 793 681| = 8 739 296 668 918 793 681

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;
  • 8 739 296 668 918 793 681 ÷ 2 = 4 369 648 334 459 396 840 + 1;
  • 4 369 648 334 459 396 840 ÷ 2 = 2 184 824 167 229 698 420 + 0;
  • 2 184 824 167 229 698 420 ÷ 2 = 1 092 412 083 614 849 210 + 0;
  • 1 092 412 083 614 849 210 ÷ 2 = 546 206 041 807 424 605 + 0;
  • 546 206 041 807 424 605 ÷ 2 = 273 103 020 903 712 302 + 1;
  • 273 103 020 903 712 302 ÷ 2 = 136 551 510 451 856 151 + 0;
  • 136 551 510 451 856 151 ÷ 2 = 68 275 755 225 928 075 + 1;
  • 68 275 755 225 928 075 ÷ 2 = 34 137 877 612 964 037 + 1;
  • 34 137 877 612 964 037 ÷ 2 = 17 068 938 806 482 018 + 1;
  • 17 068 938 806 482 018 ÷ 2 = 8 534 469 403 241 009 + 0;
  • 8 534 469 403 241 009 ÷ 2 = 4 267 234 701 620 504 + 1;
  • 4 267 234 701 620 504 ÷ 2 = 2 133 617 350 810 252 + 0;
  • 2 133 617 350 810 252 ÷ 2 = 1 066 808 675 405 126 + 0;
  • 1 066 808 675 405 126 ÷ 2 = 533 404 337 702 563 + 0;
  • 533 404 337 702 563 ÷ 2 = 266 702 168 851 281 + 1;
  • 266 702 168 851 281 ÷ 2 = 133 351 084 425 640 + 1;
  • 133 351 084 425 640 ÷ 2 = 66 675 542 212 820 + 0;
  • 66 675 542 212 820 ÷ 2 = 33 337 771 106 410 + 0;
  • 33 337 771 106 410 ÷ 2 = 16 668 885 553 205 + 0;
  • 16 668 885 553 205 ÷ 2 = 8 334 442 776 602 + 1;
  • 8 334 442 776 602 ÷ 2 = 4 167 221 388 301 + 0;
  • 4 167 221 388 301 ÷ 2 = 2 083 610 694 150 + 1;
  • 2 083 610 694 150 ÷ 2 = 1 041 805 347 075 + 0;
  • 1 041 805 347 075 ÷ 2 = 520 902 673 537 + 1;
  • 520 902 673 537 ÷ 2 = 260 451 336 768 + 1;
  • 260 451 336 768 ÷ 2 = 130 225 668 384 + 0;
  • 130 225 668 384 ÷ 2 = 65 112 834 192 + 0;
  • 65 112 834 192 ÷ 2 = 32 556 417 096 + 0;
  • 32 556 417 096 ÷ 2 = 16 278 208 548 + 0;
  • 16 278 208 548 ÷ 2 = 8 139 104 274 + 0;
  • 8 139 104 274 ÷ 2 = 4 069 552 137 + 0;
  • 4 069 552 137 ÷ 2 = 2 034 776 068 + 1;
  • 2 034 776 068 ÷ 2 = 1 017 388 034 + 0;
  • 1 017 388 034 ÷ 2 = 508 694 017 + 0;
  • 508 694 017 ÷ 2 = 254 347 008 + 1;
  • 254 347 008 ÷ 2 = 127 173 504 + 0;
  • 127 173 504 ÷ 2 = 63 586 752 + 0;
  • 63 586 752 ÷ 2 = 31 793 376 + 0;
  • 31 793 376 ÷ 2 = 15 896 688 + 0;
  • 15 896 688 ÷ 2 = 7 948 344 + 0;
  • 7 948 344 ÷ 2 = 3 974 172 + 0;
  • 3 974 172 ÷ 2 = 1 987 086 + 0;
  • 1 987 086 ÷ 2 = 993 543 + 0;
  • 993 543 ÷ 2 = 496 771 + 1;
  • 496 771 ÷ 2 = 248 385 + 1;
  • 248 385 ÷ 2 = 124 192 + 1;
  • 124 192 ÷ 2 = 62 096 + 0;
  • 62 096 ÷ 2 = 31 048 + 0;
  • 31 048 ÷ 2 = 15 524 + 0;
  • 15 524 ÷ 2 = 7 762 + 0;
  • 7 762 ÷ 2 = 3 881 + 0;
  • 3 881 ÷ 2 = 1 940 + 1;
  • 1 940 ÷ 2 = 970 + 0;
  • 970 ÷ 2 = 485 + 0;
  • 485 ÷ 2 = 242 + 1;
  • 242 ÷ 2 = 121 + 0;
  • 121 ÷ 2 = 60 + 1;
  • 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:

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

8 739 296 668 918 793 681(10) = 111 1001 0100 1000 0011 1000 0000 0100 1000 0001 1010 1000 1100 0101 1101 0001(2)

4. Determine the signed binary number bit length:

  • The base 2 number's actual length, in bits: 63.

  • 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, 63,

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.


8 739 296 668 918 793 681(10) = 0111 1001 0100 1000 0011 1000 0000 0100 1000 0001 1010 1000 1100 0101 1101 0001

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).


-8 739 296 668 918 793 681(10) = !(0111 1001 0100 1000 0011 1000 0000 0100 1000 0001 1010 1000 1100 0101 1101 0001)


Decimal Number -8 739 296 668 918 793 681(10) converted to signed binary in one's complement representation:

-8 739 296 668 918 793 681(10) = 1000 0110 1011 0111 1100 0111 1111 1011 0111 1110 0101 0111 0011 1010 0010 1110

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