One's Complement: Integer ↗ Binary: 1 110 101 011 012 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 1 110 101 011 012(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;
  • 1 110 101 011 012 ÷ 2 = 555 050 505 506 + 0;
  • 555 050 505 506 ÷ 2 = 277 525 252 753 + 0;
  • 277 525 252 753 ÷ 2 = 138 762 626 376 + 1;
  • 138 762 626 376 ÷ 2 = 69 381 313 188 + 0;
  • 69 381 313 188 ÷ 2 = 34 690 656 594 + 0;
  • 34 690 656 594 ÷ 2 = 17 345 328 297 + 0;
  • 17 345 328 297 ÷ 2 = 8 672 664 148 + 1;
  • 8 672 664 148 ÷ 2 = 4 336 332 074 + 0;
  • 4 336 332 074 ÷ 2 = 2 168 166 037 + 0;
  • 2 168 166 037 ÷ 2 = 1 084 083 018 + 1;
  • 1 084 083 018 ÷ 2 = 542 041 509 + 0;
  • 542 041 509 ÷ 2 = 271 020 754 + 1;
  • 271 020 754 ÷ 2 = 135 510 377 + 0;
  • 135 510 377 ÷ 2 = 67 755 188 + 1;
  • 67 755 188 ÷ 2 = 33 877 594 + 0;
  • 33 877 594 ÷ 2 = 16 938 797 + 0;
  • 16 938 797 ÷ 2 = 8 469 398 + 1;
  • 8 469 398 ÷ 2 = 4 234 699 + 0;
  • 4 234 699 ÷ 2 = 2 117 349 + 1;
  • 2 117 349 ÷ 2 = 1 058 674 + 1;
  • 1 058 674 ÷ 2 = 529 337 + 0;
  • 529 337 ÷ 2 = 264 668 + 1;
  • 264 668 ÷ 2 = 132 334 + 0;
  • 132 334 ÷ 2 = 66 167 + 0;
  • 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.


1 110 101 011 012(10) = 1 0000 0010 0111 0111 0010 1101 0010 1010 0100 0100(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.


Number 1 110 101 011 012(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:

1 110 101 011 012(10) = 0000 0000 0000 0000 0000 0001 0000 0010 0111 0111 0010 1101 0010 1010 0100 0100

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

The latest signed integer numbers converted from decimal system (base ten) and written as signed binary in one's complement representation

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