Convert -651 271 713 805 820 to a Signed Binary in One's (1's) Complement Representation

How to convert decimal number -651 271 713 805 820(10) to a signed binary in one's (1's) complement representation

What are the steps to convert decimal number
-651 271 713 805 820 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. Start with the positive version of the number:

|-651 271 713 805 820| = 651 271 713 805 820

2. 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;
  • 651 271 713 805 820 ÷ 2 = 325 635 856 902 910 + 0;
  • 325 635 856 902 910 ÷ 2 = 162 817 928 451 455 + 0;
  • 162 817 928 451 455 ÷ 2 = 81 408 964 225 727 + 1;
  • 81 408 964 225 727 ÷ 2 = 40 704 482 112 863 + 1;
  • 40 704 482 112 863 ÷ 2 = 20 352 241 056 431 + 1;
  • 20 352 241 056 431 ÷ 2 = 10 176 120 528 215 + 1;
  • 10 176 120 528 215 ÷ 2 = 5 088 060 264 107 + 1;
  • 5 088 060 264 107 ÷ 2 = 2 544 030 132 053 + 1;
  • 2 544 030 132 053 ÷ 2 = 1 272 015 066 026 + 1;
  • 1 272 015 066 026 ÷ 2 = 636 007 533 013 + 0;
  • 636 007 533 013 ÷ 2 = 318 003 766 506 + 1;
  • 318 003 766 506 ÷ 2 = 159 001 883 253 + 0;
  • 159 001 883 253 ÷ 2 = 79 500 941 626 + 1;
  • 79 500 941 626 ÷ 2 = 39 750 470 813 + 0;
  • 39 750 470 813 ÷ 2 = 19 875 235 406 + 1;
  • 19 875 235 406 ÷ 2 = 9 937 617 703 + 0;
  • 9 937 617 703 ÷ 2 = 4 968 808 851 + 1;
  • 4 968 808 851 ÷ 2 = 2 484 404 425 + 1;
  • 2 484 404 425 ÷ 2 = 1 242 202 212 + 1;
  • 1 242 202 212 ÷ 2 = 621 101 106 + 0;
  • 621 101 106 ÷ 2 = 310 550 553 + 0;
  • 310 550 553 ÷ 2 = 155 275 276 + 1;
  • 155 275 276 ÷ 2 = 77 637 638 + 0;
  • 77 637 638 ÷ 2 = 38 818 819 + 0;
  • 38 818 819 ÷ 2 = 19 409 409 + 1;
  • 19 409 409 ÷ 2 = 9 704 704 + 1;
  • 9 704 704 ÷ 2 = 4 852 352 + 0;
  • 4 852 352 ÷ 2 = 2 426 176 + 0;
  • 2 426 176 ÷ 2 = 1 213 088 + 0;
  • 1 213 088 ÷ 2 = 606 544 + 0;
  • 606 544 ÷ 2 = 303 272 + 0;
  • 303 272 ÷ 2 = 151 636 + 0;
  • 151 636 ÷ 2 = 75 818 + 0;
  • 75 818 ÷ 2 = 37 909 + 0;
  • 37 909 ÷ 2 = 18 954 + 1;
  • 18 954 ÷ 2 = 9 477 + 0;
  • 9 477 ÷ 2 = 4 738 + 1;
  • 4 738 ÷ 2 = 2 369 + 0;
  • 2 369 ÷ 2 = 1 184 + 1;
  • 1 184 ÷ 2 = 592 + 0;
  • 592 ÷ 2 = 296 + 0;
  • 296 ÷ 2 = 148 + 0;
  • 148 ÷ 2 = 74 + 0;
  • 74 ÷ 2 = 37 + 0;
  • 37 ÷ 2 = 18 + 1;
  • 18 ÷ 2 = 9 + 0;
  • 9 ÷ 2 = 4 + 1;
  • 4 ÷ 2 = 2 + 0;
  • 2 ÷ 2 = 1 + 0;
  • 1 ÷ 2 = 0 + 1;

3. Construct the base 2 representation of the positive number:

Take all the remainders starting from the bottom of the list constructed above.

651 271 713 805 820(10) = 10 0101 0000 0101 0100 0000 0011 0010 0111 0101 0101 1111 1100(2)

4. 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.


5. 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.


651 271 713 805 820(10) = 0000 0000 0000 0010 0101 0000 0101 0100 0000 0011 0010 0111 0101 0101 1111 1100

6. Get the negative integer number representation:

  • To write the negative integer number on 64 bits (8 Bytes), as a signed binary in one's complement representation,

  • ... Reverse all the bits from 0 to 1 and from 1 to 0 (flip the digits).


-651 271 713 805 820(10) = !(0000 0000 0000 0010 0101 0000 0101 0100 0000 0011 0010 0111 0101 0101 1111 1100)


Decimal Number -651 271 713 805 820(10) converted to signed binary in one's complement representation:

-651 271 713 805 820(10) = 1111 1111 1111 1101 1010 1111 1010 1011 1111 1100 1101 1000 1010 1010 0000 0011

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