Convert 1 111 000 999 650 to a Signed Binary in One's (1's) Complement Representation

How to convert decimal number 1 111 000 999 650(10) to a signed binary in one's (1's) complement representation

What are the steps to convert decimal number
1 111 000 999 650 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;
  • 1 111 000 999 650 ÷ 2 = 555 500 499 825 + 0;
  • 555 500 499 825 ÷ 2 = 277 750 249 912 + 1;
  • 277 750 249 912 ÷ 2 = 138 875 124 956 + 0;
  • 138 875 124 956 ÷ 2 = 69 437 562 478 + 0;
  • 69 437 562 478 ÷ 2 = 34 718 781 239 + 0;
  • 34 718 781 239 ÷ 2 = 17 359 390 619 + 1;
  • 17 359 390 619 ÷ 2 = 8 679 695 309 + 1;
  • 8 679 695 309 ÷ 2 = 4 339 847 654 + 1;
  • 4 339 847 654 ÷ 2 = 2 169 923 827 + 0;
  • 2 169 923 827 ÷ 2 = 1 084 961 913 + 1;
  • 1 084 961 913 ÷ 2 = 542 480 956 + 1;
  • 542 480 956 ÷ 2 = 271 240 478 + 0;
  • 271 240 478 ÷ 2 = 135 620 239 + 0;
  • 135 620 239 ÷ 2 = 67 810 119 + 1;
  • 67 810 119 ÷ 2 = 33 905 059 + 1;
  • 33 905 059 ÷ 2 = 16 952 529 + 1;
  • 16 952 529 ÷ 2 = 8 476 264 + 1;
  • 8 476 264 ÷ 2 = 4 238 132 + 0;
  • 4 238 132 ÷ 2 = 2 119 066 + 0;
  • 2 119 066 ÷ 2 = 1 059 533 + 0;
  • 1 059 533 ÷ 2 = 529 766 + 1;
  • 529 766 ÷ 2 = 264 883 + 0;
  • 264 883 ÷ 2 = 132 441 + 1;
  • 132 441 ÷ 2 = 66 220 + 1;
  • 66 220 ÷ 2 = 33 110 + 0;
  • 33 110 ÷ 2 = 16 555 + 0;
  • 16 555 ÷ 2 = 8 277 + 1;
  • 8 277 ÷ 2 = 4 138 + 1;
  • 4 138 ÷ 2 = 2 069 + 0;
  • 2 069 ÷ 2 = 1 034 + 1;
  • 1 034 ÷ 2 = 517 + 0;
  • 517 ÷ 2 = 258 + 1;
  • 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.

1 111 000 999 650(10) = 1 0000 0010 1010 1100 1101 0001 1110 0110 1110 0010(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.


Decimal Number 1 111 000 999 650(10) converted to signed binary in one's complement representation:

1 111 000 999 650(10) = 0000 0000 0000 0000 0000 0001 0000 0010 1010 1100 1101 0001 1110 0110 1110 0010

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