Convert -8 347 492 277 779 to a Signed Binary (Base 2)

How to convert -8 347 492 277 779(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 -8 347 492 277 779 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:

|-8 347 492 277 779| = 8 347 492 277 779

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;
  • 8 347 492 277 779 ÷ 2 = 4 173 746 138 889 + 1;
  • 4 173 746 138 889 ÷ 2 = 2 086 873 069 444 + 1;
  • 2 086 873 069 444 ÷ 2 = 1 043 436 534 722 + 0;
  • 1 043 436 534 722 ÷ 2 = 521 718 267 361 + 0;
  • 521 718 267 361 ÷ 2 = 260 859 133 680 + 1;
  • 260 859 133 680 ÷ 2 = 130 429 566 840 + 0;
  • 130 429 566 840 ÷ 2 = 65 214 783 420 + 0;
  • 65 214 783 420 ÷ 2 = 32 607 391 710 + 0;
  • 32 607 391 710 ÷ 2 = 16 303 695 855 + 0;
  • 16 303 695 855 ÷ 2 = 8 151 847 927 + 1;
  • 8 151 847 927 ÷ 2 = 4 075 923 963 + 1;
  • 4 075 923 963 ÷ 2 = 2 037 961 981 + 1;
  • 2 037 961 981 ÷ 2 = 1 018 980 990 + 1;
  • 1 018 980 990 ÷ 2 = 509 490 495 + 0;
  • 509 490 495 ÷ 2 = 254 745 247 + 1;
  • 254 745 247 ÷ 2 = 127 372 623 + 1;
  • 127 372 623 ÷ 2 = 63 686 311 + 1;
  • 63 686 311 ÷ 2 = 31 843 155 + 1;
  • 31 843 155 ÷ 2 = 15 921 577 + 1;
  • 15 921 577 ÷ 2 = 7 960 788 + 1;
  • 7 960 788 ÷ 2 = 3 980 394 + 0;
  • 3 980 394 ÷ 2 = 1 990 197 + 0;
  • 1 990 197 ÷ 2 = 995 098 + 1;
  • 995 098 ÷ 2 = 497 549 + 0;
  • 497 549 ÷ 2 = 248 774 + 1;
  • 248 774 ÷ 2 = 124 387 + 0;
  • 124 387 ÷ 2 = 62 193 + 1;
  • 62 193 ÷ 2 = 31 096 + 1;
  • 31 096 ÷ 2 = 15 548 + 0;
  • 15 548 ÷ 2 = 7 774 + 0;
  • 7 774 ÷ 2 = 3 887 + 0;
  • 3 887 ÷ 2 = 1 943 + 1;
  • 1 943 ÷ 2 = 971 + 1;
  • 971 ÷ 2 = 485 + 1;
  • 485 ÷ 2 = 242 + 1;
  • 242 ÷ 2 = 121 + 0;
  • 121 ÷ 2 = 60 + 1;
  • 60 ÷ 2 = 30 + 0;
  • 30 ÷ 2 = 15 + 0;
  • 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.

8 347 492 277 779(10) = 111 1001 0111 1000 1101 0100 1111 1101 1110 0001 0011(2)


4. Determine the signed binary number bit length:

  • The base 2 number's actual length, in bits: 43.

  • 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, 43,

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:


8 347 492 277 779(10) = 0000 0000 0000 0000 0000 0111 1001 0111 1000 1101 0100 1111 1101 1110 0001 0011

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...


-8 347 492 277 779(10) Base 10 integer number converted and written as a signed binary code (in base 2):

-8 347 492 277 779(10) = 1000 0000 0000 0000 0000 0111 1001 0111 1000 1101 0100 1111 1101 1110 0001 0011

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