Convert 1 001 101 051 709 541 255 to a Signed Binary in One's (1's) Complement Representation

How to convert decimal number 1 001 101 051 709 541 255(10) to a signed binary in one's (1's) complement representation

What are the steps to convert decimal number
1 001 101 051 709 541 255 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. 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;
  • 1 001 101 051 709 541 255 ÷ 2 = 500 550 525 854 770 627 + 1;
  • 500 550 525 854 770 627 ÷ 2 = 250 275 262 927 385 313 + 1;
  • 250 275 262 927 385 313 ÷ 2 = 125 137 631 463 692 656 + 1;
  • 125 137 631 463 692 656 ÷ 2 = 62 568 815 731 846 328 + 0;
  • 62 568 815 731 846 328 ÷ 2 = 31 284 407 865 923 164 + 0;
  • 31 284 407 865 923 164 ÷ 2 = 15 642 203 932 961 582 + 0;
  • 15 642 203 932 961 582 ÷ 2 = 7 821 101 966 480 791 + 0;
  • 7 821 101 966 480 791 ÷ 2 = 3 910 550 983 240 395 + 1;
  • 3 910 550 983 240 395 ÷ 2 = 1 955 275 491 620 197 + 1;
  • 1 955 275 491 620 197 ÷ 2 = 977 637 745 810 098 + 1;
  • 977 637 745 810 098 ÷ 2 = 488 818 872 905 049 + 0;
  • 488 818 872 905 049 ÷ 2 = 244 409 436 452 524 + 1;
  • 244 409 436 452 524 ÷ 2 = 122 204 718 226 262 + 0;
  • 122 204 718 226 262 ÷ 2 = 61 102 359 113 131 + 0;
  • 61 102 359 113 131 ÷ 2 = 30 551 179 556 565 + 1;
  • 30 551 179 556 565 ÷ 2 = 15 275 589 778 282 + 1;
  • 15 275 589 778 282 ÷ 2 = 7 637 794 889 141 + 0;
  • 7 637 794 889 141 ÷ 2 = 3 818 897 444 570 + 1;
  • 3 818 897 444 570 ÷ 2 = 1 909 448 722 285 + 0;
  • 1 909 448 722 285 ÷ 2 = 954 724 361 142 + 1;
  • 954 724 361 142 ÷ 2 = 477 362 180 571 + 0;
  • 477 362 180 571 ÷ 2 = 238 681 090 285 + 1;
  • 238 681 090 285 ÷ 2 = 119 340 545 142 + 1;
  • 119 340 545 142 ÷ 2 = 59 670 272 571 + 0;
  • 59 670 272 571 ÷ 2 = 29 835 136 285 + 1;
  • 29 835 136 285 ÷ 2 = 14 917 568 142 + 1;
  • 14 917 568 142 ÷ 2 = 7 458 784 071 + 0;
  • 7 458 784 071 ÷ 2 = 3 729 392 035 + 1;
  • 3 729 392 035 ÷ 2 = 1 864 696 017 + 1;
  • 1 864 696 017 ÷ 2 = 932 348 008 + 1;
  • 932 348 008 ÷ 2 = 466 174 004 + 0;
  • 466 174 004 ÷ 2 = 233 087 002 + 0;
  • 233 087 002 ÷ 2 = 116 543 501 + 0;
  • 116 543 501 ÷ 2 = 58 271 750 + 1;
  • 58 271 750 ÷ 2 = 29 135 875 + 0;
  • 29 135 875 ÷ 2 = 14 567 937 + 1;
  • 14 567 937 ÷ 2 = 7 283 968 + 1;
  • 7 283 968 ÷ 2 = 3 641 984 + 0;
  • 3 641 984 ÷ 2 = 1 820 992 + 0;
  • 1 820 992 ÷ 2 = 910 496 + 0;
  • 910 496 ÷ 2 = 455 248 + 0;
  • 455 248 ÷ 2 = 227 624 + 0;
  • 227 624 ÷ 2 = 113 812 + 0;
  • 113 812 ÷ 2 = 56 906 + 0;
  • 56 906 ÷ 2 = 28 453 + 0;
  • 28 453 ÷ 2 = 14 226 + 1;
  • 14 226 ÷ 2 = 7 113 + 0;
  • 7 113 ÷ 2 = 3 556 + 1;
  • 3 556 ÷ 2 = 1 778 + 0;
  • 1 778 ÷ 2 = 889 + 0;
  • 889 ÷ 2 = 444 + 1;
  • 444 ÷ 2 = 222 + 0;
  • 222 ÷ 2 = 111 + 0;
  • 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;

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

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

1 001 101 051 709 541 255(10) = 1101 1110 0100 1010 0000 0001 1010 0011 1011 0110 1010 1100 1011 1000 0111(2)

3. Determine the signed binary number bit length:

  • The base 2 number's actual length, in bits: 60.

  • 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, 60,

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

=== is: 64.


4. 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.


Decimal Number 1 001 101 051 709 541 255(10) converted to signed binary in one's complement representation:

1 001 101 051 709 541 255(10) = 0000 1101 1110 0100 1010 0000 0001 1010 0011 1011 0110 1010 1100 1011 1000 0111

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