Convert 1 000 000 000 110 903 to a Signed Binary in One's (1's) Complement Representation

How to convert decimal number 1 000 000 000 110 903(10) to a signed binary in one's (1's) complement representation

What are the steps to convert decimal number
1 000 000 000 110 903 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;
  • 1 000 000 000 110 903 ÷ 2 = 500 000 000 055 451 + 1;
  • 500 000 000 055 451 ÷ 2 = 250 000 000 027 725 + 1;
  • 250 000 000 027 725 ÷ 2 = 125 000 000 013 862 + 1;
  • 125 000 000 013 862 ÷ 2 = 62 500 000 006 931 + 0;
  • 62 500 000 006 931 ÷ 2 = 31 250 000 003 465 + 1;
  • 31 250 000 003 465 ÷ 2 = 15 625 000 001 732 + 1;
  • 15 625 000 001 732 ÷ 2 = 7 812 500 000 866 + 0;
  • 7 812 500 000 866 ÷ 2 = 3 906 250 000 433 + 0;
  • 3 906 250 000 433 ÷ 2 = 1 953 125 000 216 + 1;
  • 1 953 125 000 216 ÷ 2 = 976 562 500 108 + 0;
  • 976 562 500 108 ÷ 2 = 488 281 250 054 + 0;
  • 488 281 250 054 ÷ 2 = 244 140 625 027 + 0;
  • 244 140 625 027 ÷ 2 = 122 070 312 513 + 1;
  • 122 070 312 513 ÷ 2 = 61 035 156 256 + 1;
  • 61 035 156 256 ÷ 2 = 30 517 578 128 + 0;
  • 30 517 578 128 ÷ 2 = 15 258 789 064 + 0;
  • 15 258 789 064 ÷ 2 = 7 629 394 532 + 0;
  • 7 629 394 532 ÷ 2 = 3 814 697 266 + 0;
  • 3 814 697 266 ÷ 2 = 1 907 348 633 + 0;
  • 1 907 348 633 ÷ 2 = 953 674 316 + 1;
  • 953 674 316 ÷ 2 = 476 837 158 + 0;
  • 476 837 158 ÷ 2 = 238 418 579 + 0;
  • 238 418 579 ÷ 2 = 119 209 289 + 1;
  • 119 209 289 ÷ 2 = 59 604 644 + 1;
  • 59 604 644 ÷ 2 = 29 802 322 + 0;
  • 29 802 322 ÷ 2 = 14 901 161 + 0;
  • 14 901 161 ÷ 2 = 7 450 580 + 1;
  • 7 450 580 ÷ 2 = 3 725 290 + 0;
  • 3 725 290 ÷ 2 = 1 862 645 + 0;
  • 1 862 645 ÷ 2 = 931 322 + 1;
  • 931 322 ÷ 2 = 465 661 + 0;
  • 465 661 ÷ 2 = 232 830 + 1;
  • 232 830 ÷ 2 = 116 415 + 0;
  • 116 415 ÷ 2 = 58 207 + 1;
  • 58 207 ÷ 2 = 29 103 + 1;
  • 29 103 ÷ 2 = 14 551 + 1;
  • 14 551 ÷ 2 = 7 275 + 1;
  • 7 275 ÷ 2 = 3 637 + 1;
  • 3 637 ÷ 2 = 1 818 + 1;
  • 1 818 ÷ 2 = 909 + 0;
  • 909 ÷ 2 = 454 + 1;
  • 454 ÷ 2 = 227 + 0;
  • 227 ÷ 2 = 113 + 1;
  • 113 ÷ 2 = 56 + 1;
  • 56 ÷ 2 = 28 + 0;
  • 28 ÷ 2 = 14 + 0;
  • 14 ÷ 2 = 7 + 0;
  • 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.

1 000 000 000 110 903(10) = 11 1000 1101 0111 1110 1010 0100 1100 1000 0011 0001 0011 0111(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 1 000 000 000 110 903(10) converted to signed binary in one's complement representation:

1 000 000 000 110 903(10) = 0000 0000 0000 0011 1000 1101 0111 1110 1010 0100 1100 1000 0011 0001 0011 0111

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