Convert -476 770 269 091 693 716 to a Signed Binary (Base 2)

How to convert -476 770 269 091 693 716(10), a signed base 10 integer number? How to write it as a signed binary code in base 2

What are the required steps to convert base 10 integer
number -476 770 269 091 693 716 to signed binary code (in base 2)?

  • 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:

|-476 770 269 091 693 716| = 476 770 269 091 693 716

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;
  • 476 770 269 091 693 716 ÷ 2 = 238 385 134 545 846 858 + 0;
  • 238 385 134 545 846 858 ÷ 2 = 119 192 567 272 923 429 + 0;
  • 119 192 567 272 923 429 ÷ 2 = 59 596 283 636 461 714 + 1;
  • 59 596 283 636 461 714 ÷ 2 = 29 798 141 818 230 857 + 0;
  • 29 798 141 818 230 857 ÷ 2 = 14 899 070 909 115 428 + 1;
  • 14 899 070 909 115 428 ÷ 2 = 7 449 535 454 557 714 + 0;
  • 7 449 535 454 557 714 ÷ 2 = 3 724 767 727 278 857 + 0;
  • 3 724 767 727 278 857 ÷ 2 = 1 862 383 863 639 428 + 1;
  • 1 862 383 863 639 428 ÷ 2 = 931 191 931 819 714 + 0;
  • 931 191 931 819 714 ÷ 2 = 465 595 965 909 857 + 0;
  • 465 595 965 909 857 ÷ 2 = 232 797 982 954 928 + 1;
  • 232 797 982 954 928 ÷ 2 = 116 398 991 477 464 + 0;
  • 116 398 991 477 464 ÷ 2 = 58 199 495 738 732 + 0;
  • 58 199 495 738 732 ÷ 2 = 29 099 747 869 366 + 0;
  • 29 099 747 869 366 ÷ 2 = 14 549 873 934 683 + 0;
  • 14 549 873 934 683 ÷ 2 = 7 274 936 967 341 + 1;
  • 7 274 936 967 341 ÷ 2 = 3 637 468 483 670 + 1;
  • 3 637 468 483 670 ÷ 2 = 1 818 734 241 835 + 0;
  • 1 818 734 241 835 ÷ 2 = 909 367 120 917 + 1;
  • 909 367 120 917 ÷ 2 = 454 683 560 458 + 1;
  • 454 683 560 458 ÷ 2 = 227 341 780 229 + 0;
  • 227 341 780 229 ÷ 2 = 113 670 890 114 + 1;
  • 113 670 890 114 ÷ 2 = 56 835 445 057 + 0;
  • 56 835 445 057 ÷ 2 = 28 417 722 528 + 1;
  • 28 417 722 528 ÷ 2 = 14 208 861 264 + 0;
  • 14 208 861 264 ÷ 2 = 7 104 430 632 + 0;
  • 7 104 430 632 ÷ 2 = 3 552 215 316 + 0;
  • 3 552 215 316 ÷ 2 = 1 776 107 658 + 0;
  • 1 776 107 658 ÷ 2 = 888 053 829 + 0;
  • 888 053 829 ÷ 2 = 444 026 914 + 1;
  • 444 026 914 ÷ 2 = 222 013 457 + 0;
  • 222 013 457 ÷ 2 = 111 006 728 + 1;
  • 111 006 728 ÷ 2 = 55 503 364 + 0;
  • 55 503 364 ÷ 2 = 27 751 682 + 0;
  • 27 751 682 ÷ 2 = 13 875 841 + 0;
  • 13 875 841 ÷ 2 = 6 937 920 + 1;
  • 6 937 920 ÷ 2 = 3 468 960 + 0;
  • 3 468 960 ÷ 2 = 1 734 480 + 0;
  • 1 734 480 ÷ 2 = 867 240 + 0;
  • 867 240 ÷ 2 = 433 620 + 0;
  • 433 620 ÷ 2 = 216 810 + 0;
  • 216 810 ÷ 2 = 108 405 + 0;
  • 108 405 ÷ 2 = 54 202 + 1;
  • 54 202 ÷ 2 = 27 101 + 0;
  • 27 101 ÷ 2 = 13 550 + 1;
  • 13 550 ÷ 2 = 6 775 + 0;
  • 6 775 ÷ 2 = 3 387 + 1;
  • 3 387 ÷ 2 = 1 693 + 1;
  • 1 693 ÷ 2 = 846 + 1;
  • 846 ÷ 2 = 423 + 0;
  • 423 ÷ 2 = 211 + 1;
  • 211 ÷ 2 = 105 + 1;
  • 105 ÷ 2 = 52 + 1;
  • 52 ÷ 2 = 26 + 0;
  • 26 ÷ 2 = 13 + 0;
  • 13 ÷ 2 = 6 + 1;
  • 6 ÷ 2 = 3 + 0;
  • 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.

476 770 269 091 693 716(10) = 110 1001 1101 1101 0100 0000 1000 1010 0000 1010 1101 1000 0100 1001 0100(2)


4. Determine the signed binary number bit length:

  • The base 2 number's actual length, in bits: 59.

  • 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, 59,

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:


476 770 269 091 693 716(10) = 0000 0110 1001 1101 1101 0100 0000 1000 1010 0000 1010 1101 1000 0100 1001 0100

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...


-476 770 269 091 693 716(10) Base 10 integer number converted and written as a signed binary code (in base 2):

-476 770 269 091 693 716(10) = 1000 0110 1001 1101 1101 0100 0000 1000 1010 0000 1010 1101 1000 0100 1001 0100

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

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How to convert signed base 10 integers in decimal 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