Integer to One's Complement Binary: Number 111 011 001 072 Converted and Written as a Signed Binary in One's Complement Representation

Integer number 111 011 001 072(10) written as a signed binary in one's complement representation

How to convert the base ten signed integer number 111 011 001 072 to a signed binary in one'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.

  • To convert a base ten signed number (written as an integer in decimal system) to signed binary in one's complement representation, follow the steps below.

  • Divide the positive version of the number repeatedly by 2, keeping track of each remainder of the operations, until you get a quotient equal to 0.
  • Construct the base 2 representation using the remainders obtained, starting with the last remainder and ending with the first, in that order.
  • Construct the positive computer representation in signed binary in such a way that the first bit is 0.
  • Only if the original number is negative, reverse all the bits from 0 to 1 and from 1 to 0.
  • Below you can see the conversion process to a signed binary in one's complement representation and the related calculations.

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;
  • 111 011 001 072 ÷ 2 = 55 505 500 536 + 0;
  • 55 505 500 536 ÷ 2 = 27 752 750 268 + 0;
  • 27 752 750 268 ÷ 2 = 13 876 375 134 + 0;
  • 13 876 375 134 ÷ 2 = 6 938 187 567 + 0;
  • 6 938 187 567 ÷ 2 = 3 469 093 783 + 1;
  • 3 469 093 783 ÷ 2 = 1 734 546 891 + 1;
  • 1 734 546 891 ÷ 2 = 867 273 445 + 1;
  • 867 273 445 ÷ 2 = 433 636 722 + 1;
  • 433 636 722 ÷ 2 = 216 818 361 + 0;
  • 216 818 361 ÷ 2 = 108 409 180 + 1;
  • 108 409 180 ÷ 2 = 54 204 590 + 0;
  • 54 204 590 ÷ 2 = 27 102 295 + 0;
  • 27 102 295 ÷ 2 = 13 551 147 + 1;
  • 13 551 147 ÷ 2 = 6 775 573 + 1;
  • 6 775 573 ÷ 2 = 3 387 786 + 1;
  • 3 387 786 ÷ 2 = 1 693 893 + 0;
  • 1 693 893 ÷ 2 = 846 946 + 1;
  • 846 946 ÷ 2 = 423 473 + 0;
  • 423 473 ÷ 2 = 211 736 + 1;
  • 211 736 ÷ 2 = 105 868 + 0;
  • 105 868 ÷ 2 = 52 934 + 0;
  • 52 934 ÷ 2 = 26 467 + 0;
  • 26 467 ÷ 2 = 13 233 + 1;
  • 13 233 ÷ 2 = 6 616 + 1;
  • 6 616 ÷ 2 = 3 308 + 0;
  • 3 308 ÷ 2 = 1 654 + 0;
  • 1 654 ÷ 2 = 827 + 0;
  • 827 ÷ 2 = 413 + 1;
  • 413 ÷ 2 = 206 + 1;
  • 206 ÷ 2 = 103 + 0;
  • 103 ÷ 2 = 51 + 1;
  • 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.

111 011 001 072(10) = 1 1001 1101 1000 1100 0101 0111 0010 1111 0000(2)

3. Determine the signed binary number bit length:

  • The base 2 number's actual length, in bits: 37.

  • 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, 37,

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.


Number 111 011 001 072(10), a signed integer number (with sign), converted from decimal system (from base 10) and written as a signed binary in one's complement representation:

111 011 001 072(10) = 0000 0000 0000 0000 0000 0000 0001 1001 1101 1000 1100 0101 0111 0010 1111 0000

Spaces were used to group digits: for binary, by 4, for decimal, by 3.

» More ops: Integer number 111 011 001 089 converted and written as a signed binary in one's complement representation

» New: All the Calculations Performed by Our Visitors: Integer numbers converted and written as signed binary in one's complement representation. Data organized on a Monthly Basis

» Month 03, 2025 [March]: Integer Numbers Converted and Written as Signed Binary in One's Complement Representation. Monthly Calculations performed during the month of: March - by our visitors

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