Convert 7 995 721 801 533 to a Signed Binary in One's (1's) Complement Representation

How to convert decimal number 7 995 721 801 533(10) to a signed binary in one's (1's) complement representation

What are the steps to convert decimal number
7 995 721 801 533 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;
  • 7 995 721 801 533 ÷ 2 = 3 997 860 900 766 + 1;
  • 3 997 860 900 766 ÷ 2 = 1 998 930 450 383 + 0;
  • 1 998 930 450 383 ÷ 2 = 999 465 225 191 + 1;
  • 999 465 225 191 ÷ 2 = 499 732 612 595 + 1;
  • 499 732 612 595 ÷ 2 = 249 866 306 297 + 1;
  • 249 866 306 297 ÷ 2 = 124 933 153 148 + 1;
  • 124 933 153 148 ÷ 2 = 62 466 576 574 + 0;
  • 62 466 576 574 ÷ 2 = 31 233 288 287 + 0;
  • 31 233 288 287 ÷ 2 = 15 616 644 143 + 1;
  • 15 616 644 143 ÷ 2 = 7 808 322 071 + 1;
  • 7 808 322 071 ÷ 2 = 3 904 161 035 + 1;
  • 3 904 161 035 ÷ 2 = 1 952 080 517 + 1;
  • 1 952 080 517 ÷ 2 = 976 040 258 + 1;
  • 976 040 258 ÷ 2 = 488 020 129 + 0;
  • 488 020 129 ÷ 2 = 244 010 064 + 1;
  • 244 010 064 ÷ 2 = 122 005 032 + 0;
  • 122 005 032 ÷ 2 = 61 002 516 + 0;
  • 61 002 516 ÷ 2 = 30 501 258 + 0;
  • 30 501 258 ÷ 2 = 15 250 629 + 0;
  • 15 250 629 ÷ 2 = 7 625 314 + 1;
  • 7 625 314 ÷ 2 = 3 812 657 + 0;
  • 3 812 657 ÷ 2 = 1 906 328 + 1;
  • 1 906 328 ÷ 2 = 953 164 + 0;
  • 953 164 ÷ 2 = 476 582 + 0;
  • 476 582 ÷ 2 = 238 291 + 0;
  • 238 291 ÷ 2 = 119 145 + 1;
  • 119 145 ÷ 2 = 59 572 + 1;
  • 59 572 ÷ 2 = 29 786 + 0;
  • 29 786 ÷ 2 = 14 893 + 0;
  • 14 893 ÷ 2 = 7 446 + 1;
  • 7 446 ÷ 2 = 3 723 + 0;
  • 3 723 ÷ 2 = 1 861 + 1;
  • 1 861 ÷ 2 = 930 + 1;
  • 930 ÷ 2 = 465 + 0;
  • 465 ÷ 2 = 232 + 1;
  • 232 ÷ 2 = 116 + 0;
  • 116 ÷ 2 = 58 + 0;
  • 58 ÷ 2 = 29 + 0;
  • 29 ÷ 2 = 14 + 1;
  • 14 ÷ 2 = 7 + 0;
  • 7 ÷ 2 = 3 + 1;
  • 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.

7 995 721 801 533(10) = 111 0100 0101 1010 0110 0010 1000 0101 1111 0011 1101(2)

3. Determine the signed binary number bit length:

  • The base 2 number's actual length, in bits: 43.

  • 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, 43,

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 7 995 721 801 533(10) converted to signed binary in one's complement representation:

7 995 721 801 533(10) = 0000 0000 0000 0000 0000 0111 0100 0101 1010 0110 0010 1000 0101 1111 0011 1101

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