One's Complement: Integer ↗ Binary: 100 001 011 112 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 100 001 011 112(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;
  • 100 001 011 112 ÷ 2 = 50 000 505 556 + 0;
  • 50 000 505 556 ÷ 2 = 25 000 252 778 + 0;
  • 25 000 252 778 ÷ 2 = 12 500 126 389 + 0;
  • 12 500 126 389 ÷ 2 = 6 250 063 194 + 1;
  • 6 250 063 194 ÷ 2 = 3 125 031 597 + 0;
  • 3 125 031 597 ÷ 2 = 1 562 515 798 + 1;
  • 1 562 515 798 ÷ 2 = 781 257 899 + 0;
  • 781 257 899 ÷ 2 = 390 628 949 + 1;
  • 390 628 949 ÷ 2 = 195 314 474 + 1;
  • 195 314 474 ÷ 2 = 97 657 237 + 0;
  • 97 657 237 ÷ 2 = 48 828 618 + 1;
  • 48 828 618 ÷ 2 = 24 414 309 + 0;
  • 24 414 309 ÷ 2 = 12 207 154 + 1;
  • 12 207 154 ÷ 2 = 6 103 577 + 0;
  • 6 103 577 ÷ 2 = 3 051 788 + 1;
  • 3 051 788 ÷ 2 = 1 525 894 + 0;
  • 1 525 894 ÷ 2 = 762 947 + 0;
  • 762 947 ÷ 2 = 381 473 + 1;
  • 381 473 ÷ 2 = 190 736 + 1;
  • 190 736 ÷ 2 = 95 368 + 0;
  • 95 368 ÷ 2 = 47 684 + 0;
  • 47 684 ÷ 2 = 23 842 + 0;
  • 23 842 ÷ 2 = 11 921 + 0;
  • 11 921 ÷ 2 = 5 960 + 1;
  • 5 960 ÷ 2 = 2 980 + 0;
  • 2 980 ÷ 2 = 1 490 + 0;
  • 1 490 ÷ 2 = 745 + 0;
  • 745 ÷ 2 = 372 + 1;
  • 372 ÷ 2 = 186 + 0;
  • 186 ÷ 2 = 93 + 0;
  • 93 ÷ 2 = 46 + 1;
  • 46 ÷ 2 = 23 + 0;
  • 23 ÷ 2 = 11 + 1;
  • 11 ÷ 2 = 5 + 1;
  • 5 ÷ 2 = 2 + 1;
  • 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.


100 001 011 112(10) = 1 0111 0100 1000 1000 0110 0101 0101 1010 1000(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 100 001 011 112(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:

100 001 011 112(10) = 0000 0000 0000 0000 0000 0000 0001 0111 0100 1000 1000 0110 0101 0101 1010 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 100 001 011 111 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 100 001 011 113 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