Convert -1 342 090 341 709 541 868 to a Signed Binary in One's (1's) Complement Representation

How to convert decimal number -1 342 090 341 709 541 868(10) to a signed binary in one's (1's) complement representation

What are the steps to convert decimal number
-1 342 090 341 709 541 868 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:

|-1 342 090 341 709 541 868| = 1 342 090 341 709 541 868

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;
  • 1 342 090 341 709 541 868 ÷ 2 = 671 045 170 854 770 934 + 0;
  • 671 045 170 854 770 934 ÷ 2 = 335 522 585 427 385 467 + 0;
  • 335 522 585 427 385 467 ÷ 2 = 167 761 292 713 692 733 + 1;
  • 167 761 292 713 692 733 ÷ 2 = 83 880 646 356 846 366 + 1;
  • 83 880 646 356 846 366 ÷ 2 = 41 940 323 178 423 183 + 0;
  • 41 940 323 178 423 183 ÷ 2 = 20 970 161 589 211 591 + 1;
  • 20 970 161 589 211 591 ÷ 2 = 10 485 080 794 605 795 + 1;
  • 10 485 080 794 605 795 ÷ 2 = 5 242 540 397 302 897 + 1;
  • 5 242 540 397 302 897 ÷ 2 = 2 621 270 198 651 448 + 1;
  • 2 621 270 198 651 448 ÷ 2 = 1 310 635 099 325 724 + 0;
  • 1 310 635 099 325 724 ÷ 2 = 655 317 549 662 862 + 0;
  • 655 317 549 662 862 ÷ 2 = 327 658 774 831 431 + 0;
  • 327 658 774 831 431 ÷ 2 = 163 829 387 415 715 + 1;
  • 163 829 387 415 715 ÷ 2 = 81 914 693 707 857 + 1;
  • 81 914 693 707 857 ÷ 2 = 40 957 346 853 928 + 1;
  • 40 957 346 853 928 ÷ 2 = 20 478 673 426 964 + 0;
  • 20 478 673 426 964 ÷ 2 = 10 239 336 713 482 + 0;
  • 10 239 336 713 482 ÷ 2 = 5 119 668 356 741 + 0;
  • 5 119 668 356 741 ÷ 2 = 2 559 834 178 370 + 1;
  • 2 559 834 178 370 ÷ 2 = 1 279 917 089 185 + 0;
  • 1 279 917 089 185 ÷ 2 = 639 958 544 592 + 1;
  • 639 958 544 592 ÷ 2 = 319 979 272 296 + 0;
  • 319 979 272 296 ÷ 2 = 159 989 636 148 + 0;
  • 159 989 636 148 ÷ 2 = 79 994 818 074 + 0;
  • 79 994 818 074 ÷ 2 = 39 997 409 037 + 0;
  • 39 997 409 037 ÷ 2 = 19 998 704 518 + 1;
  • 19 998 704 518 ÷ 2 = 9 999 352 259 + 0;
  • 9 999 352 259 ÷ 2 = 4 999 676 129 + 1;
  • 4 999 676 129 ÷ 2 = 2 499 838 064 + 1;
  • 2 499 838 064 ÷ 2 = 1 249 919 032 + 0;
  • 1 249 919 032 ÷ 2 = 624 959 516 + 0;
  • 624 959 516 ÷ 2 = 312 479 758 + 0;
  • 312 479 758 ÷ 2 = 156 239 879 + 0;
  • 156 239 879 ÷ 2 = 78 119 939 + 1;
  • 78 119 939 ÷ 2 = 39 059 969 + 1;
  • 39 059 969 ÷ 2 = 19 529 984 + 1;
  • 19 529 984 ÷ 2 = 9 764 992 + 0;
  • 9 764 992 ÷ 2 = 4 882 496 + 0;
  • 4 882 496 ÷ 2 = 2 441 248 + 0;
  • 2 441 248 ÷ 2 = 1 220 624 + 0;
  • 1 220 624 ÷ 2 = 610 312 + 0;
  • 610 312 ÷ 2 = 305 156 + 0;
  • 305 156 ÷ 2 = 152 578 + 0;
  • 152 578 ÷ 2 = 76 289 + 0;
  • 76 289 ÷ 2 = 38 144 + 1;
  • 38 144 ÷ 2 = 19 072 + 0;
  • 19 072 ÷ 2 = 9 536 + 0;
  • 9 536 ÷ 2 = 4 768 + 0;
  • 4 768 ÷ 2 = 2 384 + 0;
  • 2 384 ÷ 2 = 1 192 + 0;
  • 1 192 ÷ 2 = 596 + 0;
  • 596 ÷ 2 = 298 + 0;
  • 298 ÷ 2 = 149 + 0;
  • 149 ÷ 2 = 74 + 1;
  • 74 ÷ 2 = 37 + 0;
  • 37 ÷ 2 = 18 + 1;
  • 18 ÷ 2 = 9 + 0;
  • 9 ÷ 2 = 4 + 1;
  • 4 ÷ 2 = 2 + 0;
  • 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.

1 342 090 341 709 541 868(10) = 1 0010 1010 0000 0001 0000 0000 1110 0001 1010 0001 0100 0111 0001 1110 1100(2)

4. Determine the signed binary number bit length:

  • The base 2 number's actual length, in bits: 61.

  • 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, 61,

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.


1 342 090 341 709 541 868(10) = 0001 0010 1010 0000 0001 0000 0000 1110 0001 1010 0001 0100 0111 0001 1110 1100

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).


-1 342 090 341 709 541 868(10) = !(0001 0010 1010 0000 0001 0000 0000 1110 0001 1010 0001 0100 0111 0001 1110 1100)


Decimal Number -1 342 090 341 709 541 868(10) converted to signed binary in one's complement representation:

-1 342 090 341 709 541 868(10) = 1110 1101 0101 1111 1110 1111 1111 0001 1110 0101 1110 1011 1000 1110 0001 0011

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