Convert 1 111 010 000 001 847 to a Signed Binary in One's (1's) Complement Representation

How to convert decimal number 1 111 010 000 001 847(10) to a signed binary in one's (1's) complement representation

What are the steps to convert decimal number
1 111 010 000 001 847 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;
  • 1 111 010 000 001 847 ÷ 2 = 555 505 000 000 923 + 1;
  • 555 505 000 000 923 ÷ 2 = 277 752 500 000 461 + 1;
  • 277 752 500 000 461 ÷ 2 = 138 876 250 000 230 + 1;
  • 138 876 250 000 230 ÷ 2 = 69 438 125 000 115 + 0;
  • 69 438 125 000 115 ÷ 2 = 34 719 062 500 057 + 1;
  • 34 719 062 500 057 ÷ 2 = 17 359 531 250 028 + 1;
  • 17 359 531 250 028 ÷ 2 = 8 679 765 625 014 + 0;
  • 8 679 765 625 014 ÷ 2 = 4 339 882 812 507 + 0;
  • 4 339 882 812 507 ÷ 2 = 2 169 941 406 253 + 1;
  • 2 169 941 406 253 ÷ 2 = 1 084 970 703 126 + 1;
  • 1 084 970 703 126 ÷ 2 = 542 485 351 563 + 0;
  • 542 485 351 563 ÷ 2 = 271 242 675 781 + 1;
  • 271 242 675 781 ÷ 2 = 135 621 337 890 + 1;
  • 135 621 337 890 ÷ 2 = 67 810 668 945 + 0;
  • 67 810 668 945 ÷ 2 = 33 905 334 472 + 1;
  • 33 905 334 472 ÷ 2 = 16 952 667 236 + 0;
  • 16 952 667 236 ÷ 2 = 8 476 333 618 + 0;
  • 8 476 333 618 ÷ 2 = 4 238 166 809 + 0;
  • 4 238 166 809 ÷ 2 = 2 119 083 404 + 1;
  • 2 119 083 404 ÷ 2 = 1 059 541 702 + 0;
  • 1 059 541 702 ÷ 2 = 529 770 851 + 0;
  • 529 770 851 ÷ 2 = 264 885 425 + 1;
  • 264 885 425 ÷ 2 = 132 442 712 + 1;
  • 132 442 712 ÷ 2 = 66 221 356 + 0;
  • 66 221 356 ÷ 2 = 33 110 678 + 0;
  • 33 110 678 ÷ 2 = 16 555 339 + 0;
  • 16 555 339 ÷ 2 = 8 277 669 + 1;
  • 8 277 669 ÷ 2 = 4 138 834 + 1;
  • 4 138 834 ÷ 2 = 2 069 417 + 0;
  • 2 069 417 ÷ 2 = 1 034 708 + 1;
  • 1 034 708 ÷ 2 = 517 354 + 0;
  • 517 354 ÷ 2 = 258 677 + 0;
  • 258 677 ÷ 2 = 129 338 + 1;
  • 129 338 ÷ 2 = 64 669 + 0;
  • 64 669 ÷ 2 = 32 334 + 1;
  • 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.

1 111 010 000 001 847(10) = 11 1111 0010 0111 0101 0010 1100 0110 0100 0101 1011 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 1 111 010 000 001 847(10) converted to signed binary in one's complement representation:

1 111 010 000 001 847(10) = 0000 0000 0000 0011 1111 0010 0111 0101 0010 1100 0110 0100 0101 1011 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