Convert 1 111 000 111 099 498 to a Signed Binary in One's (1's) Complement Representation

How to convert decimal number 1 111 000 111 099 498(10) to a signed binary in one's (1's) complement representation

What are the steps to convert decimal number
1 111 000 111 099 498 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;
  • 1 111 000 111 099 498 ÷ 2 = 555 500 055 549 749 + 0;
  • 555 500 055 549 749 ÷ 2 = 277 750 027 774 874 + 1;
  • 277 750 027 774 874 ÷ 2 = 138 875 013 887 437 + 0;
  • 138 875 013 887 437 ÷ 2 = 69 437 506 943 718 + 1;
  • 69 437 506 943 718 ÷ 2 = 34 718 753 471 859 + 0;
  • 34 718 753 471 859 ÷ 2 = 17 359 376 735 929 + 1;
  • 17 359 376 735 929 ÷ 2 = 8 679 688 367 964 + 1;
  • 8 679 688 367 964 ÷ 2 = 4 339 844 183 982 + 0;
  • 4 339 844 183 982 ÷ 2 = 2 169 922 091 991 + 0;
  • 2 169 922 091 991 ÷ 2 = 1 084 961 045 995 + 1;
  • 1 084 961 045 995 ÷ 2 = 542 480 522 997 + 1;
  • 542 480 522 997 ÷ 2 = 271 240 261 498 + 1;
  • 271 240 261 498 ÷ 2 = 135 620 130 749 + 0;
  • 135 620 130 749 ÷ 2 = 67 810 065 374 + 1;
  • 67 810 065 374 ÷ 2 = 33 905 032 687 + 0;
  • 33 905 032 687 ÷ 2 = 16 952 516 343 + 1;
  • 16 952 516 343 ÷ 2 = 8 476 258 171 + 1;
  • 8 476 258 171 ÷ 2 = 4 238 129 085 + 1;
  • 4 238 129 085 ÷ 2 = 2 119 064 542 + 1;
  • 2 119 064 542 ÷ 2 = 1 059 532 271 + 0;
  • 1 059 532 271 ÷ 2 = 529 766 135 + 1;
  • 529 766 135 ÷ 2 = 264 883 067 + 1;
  • 264 883 067 ÷ 2 = 132 441 533 + 1;
  • 132 441 533 ÷ 2 = 66 220 766 + 1;
  • 66 220 766 ÷ 2 = 33 110 383 + 0;
  • 33 110 383 ÷ 2 = 16 555 191 + 1;
  • 16 555 191 ÷ 2 = 8 277 595 + 1;
  • 8 277 595 ÷ 2 = 4 138 797 + 1;
  • 4 138 797 ÷ 2 = 2 069 398 + 1;
  • 2 069 398 ÷ 2 = 1 034 699 + 0;
  • 1 034 699 ÷ 2 = 517 349 + 1;
  • 517 349 ÷ 2 = 258 674 + 1;
  • 258 674 ÷ 2 = 129 337 + 0;
  • 129 337 ÷ 2 = 64 668 + 1;
  • 64 668 ÷ 2 = 32 334 + 0;
  • 32 334 ÷ 2 = 16 167 + 0;
  • 16 167 ÷ 2 = 8 083 + 1;
  • 8 083 ÷ 2 = 4 041 + 1;
  • 4 041 ÷ 2 = 2 020 + 1;
  • 2 020 ÷ 2 = 1 010 + 0;
  • 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.

1 111 000 111 099 498(10) = 11 1111 0010 0111 0010 1101 1110 1111 0111 1010 1110 0110 1010(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 1 111 000 111 099 498(10) converted to signed binary in one's complement representation:

1 111 000 111 099 498(10) = 0000 0000 0000 0011 1111 0010 0111 0010 1101 1110 1111 0111 1010 1110 0110 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