One's Complement: Integer ↗ Binary: 4 620 745 998 189 508 706 Convert the Integer Number to a Signed Binary in One's Complement Representation. Write the Base Ten Decimal System Number as a Binary Code (Written in Base Two)

Signed integer number 4 620 745 998 189 508 706(10) converted and written as a signed binary in one's complement representation (base 2) = ?

1. Divide the number repeatedly by 2:

Keep track of each remainder.

We stop when we get a quotient that is equal to zero.


  • division = quotient + remainder;
  • 4 620 745 998 189 508 706 ÷ 2 = 2 310 372 999 094 754 353 + 0;
  • 2 310 372 999 094 754 353 ÷ 2 = 1 155 186 499 547 377 176 + 1;
  • 1 155 186 499 547 377 176 ÷ 2 = 577 593 249 773 688 588 + 0;
  • 577 593 249 773 688 588 ÷ 2 = 288 796 624 886 844 294 + 0;
  • 288 796 624 886 844 294 ÷ 2 = 144 398 312 443 422 147 + 0;
  • 144 398 312 443 422 147 ÷ 2 = 72 199 156 221 711 073 + 1;
  • 72 199 156 221 711 073 ÷ 2 = 36 099 578 110 855 536 + 1;
  • 36 099 578 110 855 536 ÷ 2 = 18 049 789 055 427 768 + 0;
  • 18 049 789 055 427 768 ÷ 2 = 9 024 894 527 713 884 + 0;
  • 9 024 894 527 713 884 ÷ 2 = 4 512 447 263 856 942 + 0;
  • 4 512 447 263 856 942 ÷ 2 = 2 256 223 631 928 471 + 0;
  • 2 256 223 631 928 471 ÷ 2 = 1 128 111 815 964 235 + 1;
  • 1 128 111 815 964 235 ÷ 2 = 564 055 907 982 117 + 1;
  • 564 055 907 982 117 ÷ 2 = 282 027 953 991 058 + 1;
  • 282 027 953 991 058 ÷ 2 = 141 013 976 995 529 + 0;
  • 141 013 976 995 529 ÷ 2 = 70 506 988 497 764 + 1;
  • 70 506 988 497 764 ÷ 2 = 35 253 494 248 882 + 0;
  • 35 253 494 248 882 ÷ 2 = 17 626 747 124 441 + 0;
  • 17 626 747 124 441 ÷ 2 = 8 813 373 562 220 + 1;
  • 8 813 373 562 220 ÷ 2 = 4 406 686 781 110 + 0;
  • 4 406 686 781 110 ÷ 2 = 2 203 343 390 555 + 0;
  • 2 203 343 390 555 ÷ 2 = 1 101 671 695 277 + 1;
  • 1 101 671 695 277 ÷ 2 = 550 835 847 638 + 1;
  • 550 835 847 638 ÷ 2 = 275 417 923 819 + 0;
  • 275 417 923 819 ÷ 2 = 137 708 961 909 + 1;
  • 137 708 961 909 ÷ 2 = 68 854 480 954 + 1;
  • 68 854 480 954 ÷ 2 = 34 427 240 477 + 0;
  • 34 427 240 477 ÷ 2 = 17 213 620 238 + 1;
  • 17 213 620 238 ÷ 2 = 8 606 810 119 + 0;
  • 8 606 810 119 ÷ 2 = 4 303 405 059 + 1;
  • 4 303 405 059 ÷ 2 = 2 151 702 529 + 1;
  • 2 151 702 529 ÷ 2 = 1 075 851 264 + 1;
  • 1 075 851 264 ÷ 2 = 537 925 632 + 0;
  • 537 925 632 ÷ 2 = 268 962 816 + 0;
  • 268 962 816 ÷ 2 = 134 481 408 + 0;
  • 134 481 408 ÷ 2 = 67 240 704 + 0;
  • 67 240 704 ÷ 2 = 33 620 352 + 0;
  • 33 620 352 ÷ 2 = 16 810 176 + 0;
  • 16 810 176 ÷ 2 = 8 405 088 + 0;
  • 8 405 088 ÷ 2 = 4 202 544 + 0;
  • 4 202 544 ÷ 2 = 2 101 272 + 0;
  • 2 101 272 ÷ 2 = 1 050 636 + 0;
  • 1 050 636 ÷ 2 = 525 318 + 0;
  • 525 318 ÷ 2 = 262 659 + 0;
  • 262 659 ÷ 2 = 131 329 + 1;
  • 131 329 ÷ 2 = 65 664 + 1;
  • 65 664 ÷ 2 = 32 832 + 0;
  • 32 832 ÷ 2 = 16 416 + 0;
  • 16 416 ÷ 2 = 8 208 + 0;
  • 8 208 ÷ 2 = 4 104 + 0;
  • 4 104 ÷ 2 = 2 052 + 0;
  • 2 052 ÷ 2 = 1 026 + 0;
  • 1 026 ÷ 2 = 513 + 0;
  • 513 ÷ 2 = 256 + 1;
  • 256 ÷ 2 = 128 + 0;
  • 128 ÷ 2 = 64 + 0;
  • 64 ÷ 2 = 32 + 0;
  • 32 ÷ 2 = 16 + 0;
  • 16 ÷ 2 = 8 + 0;
  • 8 ÷ 2 = 4 + 0;
  • 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.


4 620 745 998 189 508 706(10) = 100 0000 0010 0000 0011 0000 0000 0000 1110 1011 0110 0100 1011 1000 0110 0010(2)


3. Determine the signed binary number bit length:

The base 2 number's actual length, in bits: 63.

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, 63,

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.


Number 4 620 745 998 189 508 706(10), a signed integer number (with sign), converted from decimal system (from base 10) and written as a signed binary in one's complement representation:

4 620 745 998 189 508 706(10) = 0100 0000 0010 0000 0011 0000 0000 0000 1110 1011 0110 0100 1011 1000 0110 0010

Spaces were used to group digits: for binary, by 4, for decimal, by 3.

More operations on signed integers written as signed binary numbers in one's complement representation:

» Signed integer number 4 620 745 998 189 508 705 converted from decimal system (from base 10) and written as a signed binary in one's complement representation (written in base 2) = ?

» Signed integer number 4 620 745 998 189 508 707 converted from decimal system (from base 10) and written as a signed binary in one's complement representation (written in base 2) = ?

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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