Convert 1 110 110 009 898 to a Signed Binary in One's (1's) Complement Representation

How to convert decimal number 1 110 110 009 898(10) to a signed binary in one's (1's) complement representation

What are the steps to convert decimal number
1 110 110 009 898 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;
  • 1 110 110 009 898 ÷ 2 = 555 055 004 949 + 0;
  • 555 055 004 949 ÷ 2 = 277 527 502 474 + 1;
  • 277 527 502 474 ÷ 2 = 138 763 751 237 + 0;
  • 138 763 751 237 ÷ 2 = 69 381 875 618 + 1;
  • 69 381 875 618 ÷ 2 = 34 690 937 809 + 0;
  • 34 690 937 809 ÷ 2 = 17 345 468 904 + 1;
  • 17 345 468 904 ÷ 2 = 8 672 734 452 + 0;
  • 8 672 734 452 ÷ 2 = 4 336 367 226 + 0;
  • 4 336 367 226 ÷ 2 = 2 168 183 613 + 0;
  • 2 168 183 613 ÷ 2 = 1 084 091 806 + 1;
  • 1 084 091 806 ÷ 2 = 542 045 903 + 0;
  • 542 045 903 ÷ 2 = 271 022 951 + 1;
  • 271 022 951 ÷ 2 = 135 511 475 + 1;
  • 135 511 475 ÷ 2 = 67 755 737 + 1;
  • 67 755 737 ÷ 2 = 33 877 868 + 1;
  • 33 877 868 ÷ 2 = 16 938 934 + 0;
  • 16 938 934 ÷ 2 = 8 469 467 + 0;
  • 8 469 467 ÷ 2 = 4 234 733 + 1;
  • 4 234 733 ÷ 2 = 2 117 366 + 1;
  • 2 117 366 ÷ 2 = 1 058 683 + 0;
  • 1 058 683 ÷ 2 = 529 341 + 1;
  • 529 341 ÷ 2 = 264 670 + 1;
  • 264 670 ÷ 2 = 132 335 + 0;
  • 132 335 ÷ 2 = 66 167 + 1;
  • 66 167 ÷ 2 = 33 083 + 1;
  • 33 083 ÷ 2 = 16 541 + 1;
  • 16 541 ÷ 2 = 8 270 + 1;
  • 8 270 ÷ 2 = 4 135 + 0;
  • 4 135 ÷ 2 = 2 067 + 1;
  • 2 067 ÷ 2 = 1 033 + 1;
  • 1 033 ÷ 2 = 516 + 1;
  • 516 ÷ 2 = 258 + 0;
  • 258 ÷ 2 = 129 + 0;
  • 129 ÷ 2 = 64 + 1;
  • 64 ÷ 2 = 32 + 0;
  • 32 ÷ 2 = 16 + 0;
  • 16 ÷ 2 = 8 + 0;
  • 8 ÷ 2 = 4 + 0;
  • 4 ÷ 2 = 2 + 0;
  • 2 ÷ 2 = 1 + 0;
  • 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.

1 110 110 009 898(10) = 1 0000 0010 0111 0111 1011 0110 0111 1010 0010 1010(2)

3. Determine the signed binary number bit length:

  • The base 2 number's actual length, in bits: 41.

  • 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, 41,

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 1 110 110 009 898(10) converted to signed binary in one's complement representation:

1 110 110 009 898(10) = 0000 0000 0000 0000 0000 0001 0000 0010 0111 0111 1011 0110 0111 1010 0010 1010

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