Convert 1 111 100 001 001 381 to a Signed Binary in One's (1's) Complement Representation

How to convert decimal number 1 111 100 001 001 381(10) to a signed binary in one's (1's) complement representation

What are the steps to convert decimal number
1 111 100 001 001 381 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;
  • 1 111 100 001 001 381 ÷ 2 = 555 550 000 500 690 + 1;
  • 555 550 000 500 690 ÷ 2 = 277 775 000 250 345 + 0;
  • 277 775 000 250 345 ÷ 2 = 138 887 500 125 172 + 1;
  • 138 887 500 125 172 ÷ 2 = 69 443 750 062 586 + 0;
  • 69 443 750 062 586 ÷ 2 = 34 721 875 031 293 + 0;
  • 34 721 875 031 293 ÷ 2 = 17 360 937 515 646 + 1;
  • 17 360 937 515 646 ÷ 2 = 8 680 468 757 823 + 0;
  • 8 680 468 757 823 ÷ 2 = 4 340 234 378 911 + 1;
  • 4 340 234 378 911 ÷ 2 = 2 170 117 189 455 + 1;
  • 2 170 117 189 455 ÷ 2 = 1 085 058 594 727 + 1;
  • 1 085 058 594 727 ÷ 2 = 542 529 297 363 + 1;
  • 542 529 297 363 ÷ 2 = 271 264 648 681 + 1;
  • 271 264 648 681 ÷ 2 = 135 632 324 340 + 1;
  • 135 632 324 340 ÷ 2 = 67 816 162 170 + 0;
  • 67 816 162 170 ÷ 2 = 33 908 081 085 + 0;
  • 33 908 081 085 ÷ 2 = 16 954 040 542 + 1;
  • 16 954 040 542 ÷ 2 = 8 477 020 271 + 0;
  • 8 477 020 271 ÷ 2 = 4 238 510 135 + 1;
  • 4 238 510 135 ÷ 2 = 2 119 255 067 + 1;
  • 2 119 255 067 ÷ 2 = 1 059 627 533 + 1;
  • 1 059 627 533 ÷ 2 = 529 813 766 + 1;
  • 529 813 766 ÷ 2 = 264 906 883 + 0;
  • 264 906 883 ÷ 2 = 132 453 441 + 1;
  • 132 453 441 ÷ 2 = 66 226 720 + 1;
  • 66 226 720 ÷ 2 = 33 113 360 + 0;
  • 33 113 360 ÷ 2 = 16 556 680 + 0;
  • 16 556 680 ÷ 2 = 8 278 340 + 0;
  • 8 278 340 ÷ 2 = 4 139 170 + 0;
  • 4 139 170 ÷ 2 = 2 069 585 + 0;
  • 2 069 585 ÷ 2 = 1 034 792 + 1;
  • 1 034 792 ÷ 2 = 517 396 + 0;
  • 517 396 ÷ 2 = 258 698 + 0;
  • 258 698 ÷ 2 = 129 349 + 0;
  • 129 349 ÷ 2 = 64 674 + 1;
  • 64 674 ÷ 2 = 32 337 + 0;
  • 32 337 ÷ 2 = 16 168 + 1;
  • 16 168 ÷ 2 = 8 084 + 0;
  • 8 084 ÷ 2 = 4 042 + 0;
  • 4 042 ÷ 2 = 2 021 + 0;
  • 2 021 ÷ 2 = 1 010 + 1;
  • 1 010 ÷ 2 = 505 + 0;
  • 505 ÷ 2 = 252 + 1;
  • 252 ÷ 2 = 126 + 0;
  • 126 ÷ 2 = 63 + 0;
  • 63 ÷ 2 = 31 + 1;
  • 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.

1 111 100 001 001 381(10) = 11 1111 0010 1000 1010 0010 0000 1101 1110 1001 1111 1010 0101(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.


Decimal Number 1 111 100 001 001 381(10) converted to signed binary in one's complement representation:

1 111 100 001 001 381(10) = 0000 0000 0000 0011 1111 0010 1000 1010 0010 0000 1101 1110 1001 1111 1010 0101

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