Convert 11 011 100 111 100 189 to a Signed Binary in One's (1's) Complement Representation

How to convert decimal number 11 011 100 111 100 189(10) to a signed binary in one's (1's) complement representation

What are the steps to convert decimal number
11 011 100 111 100 189 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;
  • 11 011 100 111 100 189 ÷ 2 = 5 505 550 055 550 094 + 1;
  • 5 505 550 055 550 094 ÷ 2 = 2 752 775 027 775 047 + 0;
  • 2 752 775 027 775 047 ÷ 2 = 1 376 387 513 887 523 + 1;
  • 1 376 387 513 887 523 ÷ 2 = 688 193 756 943 761 + 1;
  • 688 193 756 943 761 ÷ 2 = 344 096 878 471 880 + 1;
  • 344 096 878 471 880 ÷ 2 = 172 048 439 235 940 + 0;
  • 172 048 439 235 940 ÷ 2 = 86 024 219 617 970 + 0;
  • 86 024 219 617 970 ÷ 2 = 43 012 109 808 985 + 0;
  • 43 012 109 808 985 ÷ 2 = 21 506 054 904 492 + 1;
  • 21 506 054 904 492 ÷ 2 = 10 753 027 452 246 + 0;
  • 10 753 027 452 246 ÷ 2 = 5 376 513 726 123 + 0;
  • 5 376 513 726 123 ÷ 2 = 2 688 256 863 061 + 1;
  • 2 688 256 863 061 ÷ 2 = 1 344 128 431 530 + 1;
  • 1 344 128 431 530 ÷ 2 = 672 064 215 765 + 0;
  • 672 064 215 765 ÷ 2 = 336 032 107 882 + 1;
  • 336 032 107 882 ÷ 2 = 168 016 053 941 + 0;
  • 168 016 053 941 ÷ 2 = 84 008 026 970 + 1;
  • 84 008 026 970 ÷ 2 = 42 004 013 485 + 0;
  • 42 004 013 485 ÷ 2 = 21 002 006 742 + 1;
  • 21 002 006 742 ÷ 2 = 10 501 003 371 + 0;
  • 10 501 003 371 ÷ 2 = 5 250 501 685 + 1;
  • 5 250 501 685 ÷ 2 = 2 625 250 842 + 1;
  • 2 625 250 842 ÷ 2 = 1 312 625 421 + 0;
  • 1 312 625 421 ÷ 2 = 656 312 710 + 1;
  • 656 312 710 ÷ 2 = 328 156 355 + 0;
  • 328 156 355 ÷ 2 = 164 078 177 + 1;
  • 164 078 177 ÷ 2 = 82 039 088 + 1;
  • 82 039 088 ÷ 2 = 41 019 544 + 0;
  • 41 019 544 ÷ 2 = 20 509 772 + 0;
  • 20 509 772 ÷ 2 = 10 254 886 + 0;
  • 10 254 886 ÷ 2 = 5 127 443 + 0;
  • 5 127 443 ÷ 2 = 2 563 721 + 1;
  • 2 563 721 ÷ 2 = 1 281 860 + 1;
  • 1 281 860 ÷ 2 = 640 930 + 0;
  • 640 930 ÷ 2 = 320 465 + 0;
  • 320 465 ÷ 2 = 160 232 + 1;
  • 160 232 ÷ 2 = 80 116 + 0;
  • 80 116 ÷ 2 = 40 058 + 0;
  • 40 058 ÷ 2 = 20 029 + 0;
  • 20 029 ÷ 2 = 10 014 + 1;
  • 10 014 ÷ 2 = 5 007 + 0;
  • 5 007 ÷ 2 = 2 503 + 1;
  • 2 503 ÷ 2 = 1 251 + 1;
  • 1 251 ÷ 2 = 625 + 1;
  • 625 ÷ 2 = 312 + 1;
  • 312 ÷ 2 = 156 + 0;
  • 156 ÷ 2 = 78 + 0;
  • 78 ÷ 2 = 39 + 0;
  • 39 ÷ 2 = 19 + 1;
  • 19 ÷ 2 = 9 + 1;
  • 9 ÷ 2 = 4 + 1;
  • 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.

11 011 100 111 100 189(10) = 10 0111 0001 1110 1000 1001 1000 0110 1011 0101 0101 1001 0001 1101(2)

3. Determine the signed binary number bit length:

  • The base 2 number's actual length, in bits: 54.

  • 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, 54,

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 11 011 100 111 100 189(10) converted to signed binary in one's complement representation:

11 011 100 111 100 189(10) = 0000 0000 0010 0111 0001 1110 1000 1001 1000 0110 1011 0101 0101 1001 0001 1101

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