Convert 100 110 101 082 to a Signed Binary in One's (1's) Complement Representation

How to convert decimal number 100 110 101 082(10) to a signed binary in one's (1's) complement representation

What are the steps to convert decimal number
100 110 101 082 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;
  • 100 110 101 082 ÷ 2 = 50 055 050 541 + 0;
  • 50 055 050 541 ÷ 2 = 25 027 525 270 + 1;
  • 25 027 525 270 ÷ 2 = 12 513 762 635 + 0;
  • 12 513 762 635 ÷ 2 = 6 256 881 317 + 1;
  • 6 256 881 317 ÷ 2 = 3 128 440 658 + 1;
  • 3 128 440 658 ÷ 2 = 1 564 220 329 + 0;
  • 1 564 220 329 ÷ 2 = 782 110 164 + 1;
  • 782 110 164 ÷ 2 = 391 055 082 + 0;
  • 391 055 082 ÷ 2 = 195 527 541 + 0;
  • 195 527 541 ÷ 2 = 97 763 770 + 1;
  • 97 763 770 ÷ 2 = 48 881 885 + 0;
  • 48 881 885 ÷ 2 = 24 440 942 + 1;
  • 24 440 942 ÷ 2 = 12 220 471 + 0;
  • 12 220 471 ÷ 2 = 6 110 235 + 1;
  • 6 110 235 ÷ 2 = 3 055 117 + 1;
  • 3 055 117 ÷ 2 = 1 527 558 + 1;
  • 1 527 558 ÷ 2 = 763 779 + 0;
  • 763 779 ÷ 2 = 381 889 + 1;
  • 381 889 ÷ 2 = 190 944 + 1;
  • 190 944 ÷ 2 = 95 472 + 0;
  • 95 472 ÷ 2 = 47 736 + 0;
  • 47 736 ÷ 2 = 23 868 + 0;
  • 23 868 ÷ 2 = 11 934 + 0;
  • 11 934 ÷ 2 = 5 967 + 0;
  • 5 967 ÷ 2 = 2 983 + 1;
  • 2 983 ÷ 2 = 1 491 + 1;
  • 1 491 ÷ 2 = 745 + 1;
  • 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.

100 110 101 082(10) = 1 0111 0100 1111 0000 0110 1110 1010 0101 1010(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.


Decimal Number 100 110 101 082(10) converted to signed binary in one's complement representation:

100 110 101 082(10) = 0000 0000 0000 0000 0000 0000 0001 0111 0100 1111 0000 0110 1110 1010 0101 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