One's Complement: Integer ↗ Binary: 1 101 100 101 110 056 Convert the Integer Number to a Signed Binary in One's Complement Representation. Write the Base Ten Decimal System Number as a Binary Code (Written in Base Two)

Signed integer number 1 101 100 101 110 056(10) converted and written as a signed binary in one's complement representation (base 2) = ?

1. Divide the number repeatedly by 2:

Keep track of each remainder.

We stop when we get a quotient that is equal to zero.


  • division = quotient + remainder;
  • 1 101 100 101 110 056 ÷ 2 = 550 550 050 555 028 + 0;
  • 550 550 050 555 028 ÷ 2 = 275 275 025 277 514 + 0;
  • 275 275 025 277 514 ÷ 2 = 137 637 512 638 757 + 0;
  • 137 637 512 638 757 ÷ 2 = 68 818 756 319 378 + 1;
  • 68 818 756 319 378 ÷ 2 = 34 409 378 159 689 + 0;
  • 34 409 378 159 689 ÷ 2 = 17 204 689 079 844 + 1;
  • 17 204 689 079 844 ÷ 2 = 8 602 344 539 922 + 0;
  • 8 602 344 539 922 ÷ 2 = 4 301 172 269 961 + 0;
  • 4 301 172 269 961 ÷ 2 = 2 150 586 134 980 + 1;
  • 2 150 586 134 980 ÷ 2 = 1 075 293 067 490 + 0;
  • 1 075 293 067 490 ÷ 2 = 537 646 533 745 + 0;
  • 537 646 533 745 ÷ 2 = 268 823 266 872 + 1;
  • 268 823 266 872 ÷ 2 = 134 411 633 436 + 0;
  • 134 411 633 436 ÷ 2 = 67 205 816 718 + 0;
  • 67 205 816 718 ÷ 2 = 33 602 908 359 + 0;
  • 33 602 908 359 ÷ 2 = 16 801 454 179 + 1;
  • 16 801 454 179 ÷ 2 = 8 400 727 089 + 1;
  • 8 400 727 089 ÷ 2 = 4 200 363 544 + 1;
  • 4 200 363 544 ÷ 2 = 2 100 181 772 + 0;
  • 2 100 181 772 ÷ 2 = 1 050 090 886 + 0;
  • 1 050 090 886 ÷ 2 = 525 045 443 + 0;
  • 525 045 443 ÷ 2 = 262 522 721 + 1;
  • 262 522 721 ÷ 2 = 131 261 360 + 1;
  • 131 261 360 ÷ 2 = 65 630 680 + 0;
  • 65 630 680 ÷ 2 = 32 815 340 + 0;
  • 32 815 340 ÷ 2 = 16 407 670 + 0;
  • 16 407 670 ÷ 2 = 8 203 835 + 0;
  • 8 203 835 ÷ 2 = 4 101 917 + 1;
  • 4 101 917 ÷ 2 = 2 050 958 + 1;
  • 2 050 958 ÷ 2 = 1 025 479 + 0;
  • 1 025 479 ÷ 2 = 512 739 + 1;
  • 512 739 ÷ 2 = 256 369 + 1;
  • 256 369 ÷ 2 = 128 184 + 1;
  • 128 184 ÷ 2 = 64 092 + 0;
  • 64 092 ÷ 2 = 32 046 + 0;
  • 32 046 ÷ 2 = 16 023 + 0;
  • 16 023 ÷ 2 = 8 011 + 1;
  • 8 011 ÷ 2 = 4 005 + 1;
  • 4 005 ÷ 2 = 2 002 + 1;
  • 2 002 ÷ 2 = 1 001 + 0;
  • 1 001 ÷ 2 = 500 + 1;
  • 500 ÷ 2 = 250 + 0;
  • 250 ÷ 2 = 125 + 0;
  • 125 ÷ 2 = 62 + 1;
  • 62 ÷ 2 = 31 + 0;
  • 31 ÷ 2 = 15 + 1;
  • 15 ÷ 2 = 7 + 1;
  • 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.


1 101 100 101 110 056(10) = 11 1110 1001 0111 0001 1101 1000 0110 0011 1000 1001 0010 1000(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.


Number 1 101 100 101 110 056(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:

1 101 100 101 110 056(10) = 0000 0000 0000 0011 1110 1001 0111 0001 1101 1000 0110 0011 1000 1001 0010 1000

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

More operations on signed integers written as signed binary numbers in one's complement representation:

» Signed integer number 1 101 100 101 110 055 converted from decimal system (from base 10) and written as a signed binary in one's complement representation (written in base 2) = ?

» Signed integer number 1 101 100 101 110 057 converted from decimal system (from base 10) and written as a signed binary in one's complement representation (written in base 2) = ?

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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