Convert 647 288 676 734 879 to a Signed Binary in One's (1's) Complement Representation

How to convert decimal number 647 288 676 734 879(10) to a signed binary in one's (1's) complement representation

What are the steps to convert decimal number
647 288 676 734 879 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;
  • 647 288 676 734 879 ÷ 2 = 323 644 338 367 439 + 1;
  • 323 644 338 367 439 ÷ 2 = 161 822 169 183 719 + 1;
  • 161 822 169 183 719 ÷ 2 = 80 911 084 591 859 + 1;
  • 80 911 084 591 859 ÷ 2 = 40 455 542 295 929 + 1;
  • 40 455 542 295 929 ÷ 2 = 20 227 771 147 964 + 1;
  • 20 227 771 147 964 ÷ 2 = 10 113 885 573 982 + 0;
  • 10 113 885 573 982 ÷ 2 = 5 056 942 786 991 + 0;
  • 5 056 942 786 991 ÷ 2 = 2 528 471 393 495 + 1;
  • 2 528 471 393 495 ÷ 2 = 1 264 235 696 747 + 1;
  • 1 264 235 696 747 ÷ 2 = 632 117 848 373 + 1;
  • 632 117 848 373 ÷ 2 = 316 058 924 186 + 1;
  • 316 058 924 186 ÷ 2 = 158 029 462 093 + 0;
  • 158 029 462 093 ÷ 2 = 79 014 731 046 + 1;
  • 79 014 731 046 ÷ 2 = 39 507 365 523 + 0;
  • 39 507 365 523 ÷ 2 = 19 753 682 761 + 1;
  • 19 753 682 761 ÷ 2 = 9 876 841 380 + 1;
  • 9 876 841 380 ÷ 2 = 4 938 420 690 + 0;
  • 4 938 420 690 ÷ 2 = 2 469 210 345 + 0;
  • 2 469 210 345 ÷ 2 = 1 234 605 172 + 1;
  • 1 234 605 172 ÷ 2 = 617 302 586 + 0;
  • 617 302 586 ÷ 2 = 308 651 293 + 0;
  • 308 651 293 ÷ 2 = 154 325 646 + 1;
  • 154 325 646 ÷ 2 = 77 162 823 + 0;
  • 77 162 823 ÷ 2 = 38 581 411 + 1;
  • 38 581 411 ÷ 2 = 19 290 705 + 1;
  • 19 290 705 ÷ 2 = 9 645 352 + 1;
  • 9 645 352 ÷ 2 = 4 822 676 + 0;
  • 4 822 676 ÷ 2 = 2 411 338 + 0;
  • 2 411 338 ÷ 2 = 1 205 669 + 0;
  • 1 205 669 ÷ 2 = 602 834 + 1;
  • 602 834 ÷ 2 = 301 417 + 0;
  • 301 417 ÷ 2 = 150 708 + 1;
  • 150 708 ÷ 2 = 75 354 + 0;
  • 75 354 ÷ 2 = 37 677 + 0;
  • 37 677 ÷ 2 = 18 838 + 1;
  • 18 838 ÷ 2 = 9 419 + 0;
  • 9 419 ÷ 2 = 4 709 + 1;
  • 4 709 ÷ 2 = 2 354 + 1;
  • 2 354 ÷ 2 = 1 177 + 0;
  • 1 177 ÷ 2 = 588 + 1;
  • 588 ÷ 2 = 294 + 0;
  • 294 ÷ 2 = 147 + 0;
  • 147 ÷ 2 = 73 + 1;
  • 73 ÷ 2 = 36 + 1;
  • 36 ÷ 2 = 18 + 0;
  • 18 ÷ 2 = 9 + 0;
  • 9 ÷ 2 = 4 + 1;
  • 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.

647 288 676 734 879(10) = 10 0100 1100 1011 0100 1010 0011 1010 0100 1101 0111 1001 1111(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 647 288 676 734 879(10) converted to signed binary in one's complement representation:

647 288 676 734 879(10) = 0000 0000 0000 0010 0100 1100 1011 0100 1010 0011 1010 0100 1101 0111 1001 1111

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