Convert 444 561 713 799 180 to a Signed Binary in One's (1's) Complement Representation

How to convert decimal number 444 561 713 799 180(10) to a signed binary in one's (1's) complement representation

What are the steps to convert decimal number
444 561 713 799 180 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;
  • 444 561 713 799 180 ÷ 2 = 222 280 856 899 590 + 0;
  • 222 280 856 899 590 ÷ 2 = 111 140 428 449 795 + 0;
  • 111 140 428 449 795 ÷ 2 = 55 570 214 224 897 + 1;
  • 55 570 214 224 897 ÷ 2 = 27 785 107 112 448 + 1;
  • 27 785 107 112 448 ÷ 2 = 13 892 553 556 224 + 0;
  • 13 892 553 556 224 ÷ 2 = 6 946 276 778 112 + 0;
  • 6 946 276 778 112 ÷ 2 = 3 473 138 389 056 + 0;
  • 3 473 138 389 056 ÷ 2 = 1 736 569 194 528 + 0;
  • 1 736 569 194 528 ÷ 2 = 868 284 597 264 + 0;
  • 868 284 597 264 ÷ 2 = 434 142 298 632 + 0;
  • 434 142 298 632 ÷ 2 = 217 071 149 316 + 0;
  • 217 071 149 316 ÷ 2 = 108 535 574 658 + 0;
  • 108 535 574 658 ÷ 2 = 54 267 787 329 + 0;
  • 54 267 787 329 ÷ 2 = 27 133 893 664 + 1;
  • 27 133 893 664 ÷ 2 = 13 566 946 832 + 0;
  • 13 566 946 832 ÷ 2 = 6 783 473 416 + 0;
  • 6 783 473 416 ÷ 2 = 3 391 736 708 + 0;
  • 3 391 736 708 ÷ 2 = 1 695 868 354 + 0;
  • 1 695 868 354 ÷ 2 = 847 934 177 + 0;
  • 847 934 177 ÷ 2 = 423 967 088 + 1;
  • 423 967 088 ÷ 2 = 211 983 544 + 0;
  • 211 983 544 ÷ 2 = 105 991 772 + 0;
  • 105 991 772 ÷ 2 = 52 995 886 + 0;
  • 52 995 886 ÷ 2 = 26 497 943 + 0;
  • 26 497 943 ÷ 2 = 13 248 971 + 1;
  • 13 248 971 ÷ 2 = 6 624 485 + 1;
  • 6 624 485 ÷ 2 = 3 312 242 + 1;
  • 3 312 242 ÷ 2 = 1 656 121 + 0;
  • 1 656 121 ÷ 2 = 828 060 + 1;
  • 828 060 ÷ 2 = 414 030 + 0;
  • 414 030 ÷ 2 = 207 015 + 0;
  • 207 015 ÷ 2 = 103 507 + 1;
  • 103 507 ÷ 2 = 51 753 + 1;
  • 51 753 ÷ 2 = 25 876 + 1;
  • 25 876 ÷ 2 = 12 938 + 0;
  • 12 938 ÷ 2 = 6 469 + 0;
  • 6 469 ÷ 2 = 3 234 + 1;
  • 3 234 ÷ 2 = 1 617 + 0;
  • 1 617 ÷ 2 = 808 + 1;
  • 808 ÷ 2 = 404 + 0;
  • 404 ÷ 2 = 202 + 0;
  • 202 ÷ 2 = 101 + 0;
  • 101 ÷ 2 = 50 + 1;
  • 50 ÷ 2 = 25 + 0;
  • 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.

444 561 713 799 180(10) = 1 1001 0100 0101 0011 1001 0111 0000 1000 0010 0000 0000 1100(2)

3. Determine the signed binary number bit length:

  • The base 2 number's actual length, in bits: 49.

  • 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, 49,

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 444 561 713 799 180(10) converted to signed binary in one's complement representation:

444 561 713 799 180(10) = 0000 0000 0000 0001 1001 0100 0101 0011 1001 0111 0000 1000 0010 0000 0000 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