Convert 901 031 709 543 205 to a Signed Binary in One's (1's) Complement Representation

How to convert decimal number 901 031 709 543 205(10) to a signed binary in one's (1's) complement representation

What are the steps to convert decimal number
901 031 709 543 205 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;
  • 901 031 709 543 205 ÷ 2 = 450 515 854 771 602 + 1;
  • 450 515 854 771 602 ÷ 2 = 225 257 927 385 801 + 0;
  • 225 257 927 385 801 ÷ 2 = 112 628 963 692 900 + 1;
  • 112 628 963 692 900 ÷ 2 = 56 314 481 846 450 + 0;
  • 56 314 481 846 450 ÷ 2 = 28 157 240 923 225 + 0;
  • 28 157 240 923 225 ÷ 2 = 14 078 620 461 612 + 1;
  • 14 078 620 461 612 ÷ 2 = 7 039 310 230 806 + 0;
  • 7 039 310 230 806 ÷ 2 = 3 519 655 115 403 + 0;
  • 3 519 655 115 403 ÷ 2 = 1 759 827 557 701 + 1;
  • 1 759 827 557 701 ÷ 2 = 879 913 778 850 + 1;
  • 879 913 778 850 ÷ 2 = 439 956 889 425 + 0;
  • 439 956 889 425 ÷ 2 = 219 978 444 712 + 1;
  • 219 978 444 712 ÷ 2 = 109 989 222 356 + 0;
  • 109 989 222 356 ÷ 2 = 54 994 611 178 + 0;
  • 54 994 611 178 ÷ 2 = 27 497 305 589 + 0;
  • 27 497 305 589 ÷ 2 = 13 748 652 794 + 1;
  • 13 748 652 794 ÷ 2 = 6 874 326 397 + 0;
  • 6 874 326 397 ÷ 2 = 3 437 163 198 + 1;
  • 3 437 163 198 ÷ 2 = 1 718 581 599 + 0;
  • 1 718 581 599 ÷ 2 = 859 290 799 + 1;
  • 859 290 799 ÷ 2 = 429 645 399 + 1;
  • 429 645 399 ÷ 2 = 214 822 699 + 1;
  • 214 822 699 ÷ 2 = 107 411 349 + 1;
  • 107 411 349 ÷ 2 = 53 705 674 + 1;
  • 53 705 674 ÷ 2 = 26 852 837 + 0;
  • 26 852 837 ÷ 2 = 13 426 418 + 1;
  • 13 426 418 ÷ 2 = 6 713 209 + 0;
  • 6 713 209 ÷ 2 = 3 356 604 + 1;
  • 3 356 604 ÷ 2 = 1 678 302 + 0;
  • 1 678 302 ÷ 2 = 839 151 + 0;
  • 839 151 ÷ 2 = 419 575 + 1;
  • 419 575 ÷ 2 = 209 787 + 1;
  • 209 787 ÷ 2 = 104 893 + 1;
  • 104 893 ÷ 2 = 52 446 + 1;
  • 52 446 ÷ 2 = 26 223 + 0;
  • 26 223 ÷ 2 = 13 111 + 1;
  • 13 111 ÷ 2 = 6 555 + 1;
  • 6 555 ÷ 2 = 3 277 + 1;
  • 3 277 ÷ 2 = 1 638 + 1;
  • 1 638 ÷ 2 = 819 + 0;
  • 819 ÷ 2 = 409 + 1;
  • 409 ÷ 2 = 204 + 1;
  • 204 ÷ 2 = 102 + 0;
  • 102 ÷ 2 = 51 + 0;
  • 51 ÷ 2 = 25 + 1;
  • 25 ÷ 2 = 12 + 1;
  • 12 ÷ 2 = 6 + 0;
  • 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.

901 031 709 543 205(10) = 11 0011 0011 0111 1011 1100 1010 1111 1010 1000 1011 0010 0101(2)

3. Determine the signed binary number bit length:

  • The base 2 number's actual length, in bits: 50.

  • 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, 50,

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 901 031 709 543 205(10) converted to signed binary in one's complement representation:

901 031 709 543 205(10) = 0000 0000 0000 0011 0011 0011 0111 1011 1100 1010 1111 1010 1000 1011 0010 0101

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