Integer to Signed Binary: Number -4 608 353 354 703 133 778 Converted and Written as a Signed Binary. Base Ten Decimal System Conversion

Integer number -4 608 353 354 703 133 778(10) written as a signed binary number

1. Start with the positive version of the number:

|-4 608 353 354 703 133 778| = 4 608 353 354 703 133 778

2. 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;
  • 4 608 353 354 703 133 778 ÷ 2 = 2 304 176 677 351 566 889 + 0;
  • 2 304 176 677 351 566 889 ÷ 2 = 1 152 088 338 675 783 444 + 1;
  • 1 152 088 338 675 783 444 ÷ 2 = 576 044 169 337 891 722 + 0;
  • 576 044 169 337 891 722 ÷ 2 = 288 022 084 668 945 861 + 0;
  • 288 022 084 668 945 861 ÷ 2 = 144 011 042 334 472 930 + 1;
  • 144 011 042 334 472 930 ÷ 2 = 72 005 521 167 236 465 + 0;
  • 72 005 521 167 236 465 ÷ 2 = 36 002 760 583 618 232 + 1;
  • 36 002 760 583 618 232 ÷ 2 = 18 001 380 291 809 116 + 0;
  • 18 001 380 291 809 116 ÷ 2 = 9 000 690 145 904 558 + 0;
  • 9 000 690 145 904 558 ÷ 2 = 4 500 345 072 952 279 + 0;
  • 4 500 345 072 952 279 ÷ 2 = 2 250 172 536 476 139 + 1;
  • 2 250 172 536 476 139 ÷ 2 = 1 125 086 268 238 069 + 1;
  • 1 125 086 268 238 069 ÷ 2 = 562 543 134 119 034 + 1;
  • 562 543 134 119 034 ÷ 2 = 281 271 567 059 517 + 0;
  • 281 271 567 059 517 ÷ 2 = 140 635 783 529 758 + 1;
  • 140 635 783 529 758 ÷ 2 = 70 317 891 764 879 + 0;
  • 70 317 891 764 879 ÷ 2 = 35 158 945 882 439 + 1;
  • 35 158 945 882 439 ÷ 2 = 17 579 472 941 219 + 1;
  • 17 579 472 941 219 ÷ 2 = 8 789 736 470 609 + 1;
  • 8 789 736 470 609 ÷ 2 = 4 394 868 235 304 + 1;
  • 4 394 868 235 304 ÷ 2 = 2 197 434 117 652 + 0;
  • 2 197 434 117 652 ÷ 2 = 1 098 717 058 826 + 0;
  • 1 098 717 058 826 ÷ 2 = 549 358 529 413 + 0;
  • 549 358 529 413 ÷ 2 = 274 679 264 706 + 1;
  • 274 679 264 706 ÷ 2 = 137 339 632 353 + 0;
  • 137 339 632 353 ÷ 2 = 68 669 816 176 + 1;
  • 68 669 816 176 ÷ 2 = 34 334 908 088 + 0;
  • 34 334 908 088 ÷ 2 = 17 167 454 044 + 0;
  • 17 167 454 044 ÷ 2 = 8 583 727 022 + 0;
  • 8 583 727 022 ÷ 2 = 4 291 863 511 + 0;
  • 4 291 863 511 ÷ 2 = 2 145 931 755 + 1;
  • 2 145 931 755 ÷ 2 = 1 072 965 877 + 1;
  • 1 072 965 877 ÷ 2 = 536 482 938 + 1;
  • 536 482 938 ÷ 2 = 268 241 469 + 0;
  • 268 241 469 ÷ 2 = 134 120 734 + 1;
  • 134 120 734 ÷ 2 = 67 060 367 + 0;
  • 67 060 367 ÷ 2 = 33 530 183 + 1;
  • 33 530 183 ÷ 2 = 16 765 091 + 1;
  • 16 765 091 ÷ 2 = 8 382 545 + 1;
  • 8 382 545 ÷ 2 = 4 191 272 + 1;
  • 4 191 272 ÷ 2 = 2 095 636 + 0;
  • 2 095 636 ÷ 2 = 1 047 818 + 0;
  • 1 047 818 ÷ 2 = 523 909 + 0;
  • 523 909 ÷ 2 = 261 954 + 1;
  • 261 954 ÷ 2 = 130 977 + 0;
  • 130 977 ÷ 2 = 65 488 + 1;
  • 65 488 ÷ 2 = 32 744 + 0;
  • 32 744 ÷ 2 = 16 372 + 0;
  • 16 372 ÷ 2 = 8 186 + 0;
  • 8 186 ÷ 2 = 4 093 + 0;
  • 4 093 ÷ 2 = 2 046 + 1;
  • 2 046 ÷ 2 = 1 023 + 0;
  • 1 023 ÷ 2 = 511 + 1;
  • 511 ÷ 2 = 255 + 1;
  • 255 ÷ 2 = 127 + 1;
  • 127 ÷ 2 = 63 + 1;
  • 63 ÷ 2 = 31 + 1;
  • 31 ÷ 2 = 15 + 1;
  • 15 ÷ 2 = 7 + 1;
  • 7 ÷ 2 = 3 + 1;
  • 3 ÷ 2 = 1 + 1;
  • 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.

4 608 353 354 703 133 778(10) = 11 1111 1111 0100 0010 1000 1111 0101 1100 0010 1000 1111 0101 1100 0101 0010(2)


4. Determine the signed binary number bit length:

The base 2 number's actual length, in bits: 62.

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) is reserved for 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, 62,

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:


4 608 353 354 703 133 778(10) = 0011 1111 1111 0100 0010 1000 1111 0101 1100 0010 1000 1111 0101 1100 0101 0010

6. Get the negative integer number representation:

To get the negative integer number representation on 64 bits (8 Bytes),

... change the first bit (the leftmost), from 0 to 1...


Number -4 608 353 354 703 133 778(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):

-4 608 353 354 703 133 778(10) = 1011 1111 1111 0100 0010 1000 1111 0101 1100 0010 1000 1111 0101 1100 0101 0010

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

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How to convert signed integers from decimal system to binary code system

Follow the steps below to convert a signed base ten integer number to signed binary:

  • 1. In a signed binary, first bit (the leftmost) is reserved for sign: 0 = positive integer number, 1 = positive integer number. If the number to be converted is negative, start with its positive version.
  • 2. Divide repeatedly by 2 the positive integer number keeping track of each remainder. STOP when we get a quotient that is 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 have a length of 4, 8, 16, 32, 64, ... bits (power of 2) - if needed, fill in extra '0' bits in front of the base 2 number (to the left), up to the right length; this way the first bit (the leftmost one) is always '0', as for a positive representation.
  • 5. To get the negative reprezentation of the number, simply switch the first bit (the leftmost one), from '0' to '1'.

Example: convert the negative number -63 from decimal system (base ten) to signed binary code system:

  • 1. Start with the positive version of the number: |-63| = 63;
  • 2. Divide repeatedly 63 by 2, keeping track of each remainder, until we get a quotient that is equal to zero:
    • division = quotient + remainder
    • 63 ÷ 2 = 31 + 1
    • 31 ÷ 2 = 15 + 1
    • 15 ÷ 2 = 7 + 1
    • 7 ÷ 2 = 3 + 1
    • 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:
    63(10) = 11 1111(2)
  • 4. The actual length of base 2 representation number is 6, so the positive binary computer representation length of the signed binary will take in this case 8 bits (the least power of 2 higher than 6) - add extra '0's in front (to the left), up to the required length; this way the first bit (the leftmost one) is to be '0', as for a positive number:
    63(10) = 0011 1111(2)
  • 5. To get the negative integer number representation simply change the first bit (the leftmost), from '0' to '1':
    -63(10) = 1011 1111
  • Number -63(10), signed integer, converted from decimal system (base 10) to signed binary = 1011 1111