Convert -36 170 086 410 616 699 to a Signed Binary (Base 2)

How to convert -36 170 086 410 616 699(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 -36 170 086 410 616 699 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:

|-36 170 086 410 616 699| = 36 170 086 410 616 699

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;
  • 36 170 086 410 616 699 ÷ 2 = 18 085 043 205 308 349 + 1;
  • 18 085 043 205 308 349 ÷ 2 = 9 042 521 602 654 174 + 1;
  • 9 042 521 602 654 174 ÷ 2 = 4 521 260 801 327 087 + 0;
  • 4 521 260 801 327 087 ÷ 2 = 2 260 630 400 663 543 + 1;
  • 2 260 630 400 663 543 ÷ 2 = 1 130 315 200 331 771 + 1;
  • 1 130 315 200 331 771 ÷ 2 = 565 157 600 165 885 + 1;
  • 565 157 600 165 885 ÷ 2 = 282 578 800 082 942 + 1;
  • 282 578 800 082 942 ÷ 2 = 141 289 400 041 471 + 0;
  • 141 289 400 041 471 ÷ 2 = 70 644 700 020 735 + 1;
  • 70 644 700 020 735 ÷ 2 = 35 322 350 010 367 + 1;
  • 35 322 350 010 367 ÷ 2 = 17 661 175 005 183 + 1;
  • 17 661 175 005 183 ÷ 2 = 8 830 587 502 591 + 1;
  • 8 830 587 502 591 ÷ 2 = 4 415 293 751 295 + 1;
  • 4 415 293 751 295 ÷ 2 = 2 207 646 875 647 + 1;
  • 2 207 646 875 647 ÷ 2 = 1 103 823 437 823 + 1;
  • 1 103 823 437 823 ÷ 2 = 551 911 718 911 + 1;
  • 551 911 718 911 ÷ 2 = 275 955 859 455 + 1;
  • 275 955 859 455 ÷ 2 = 137 977 929 727 + 1;
  • 137 977 929 727 ÷ 2 = 68 988 964 863 + 1;
  • 68 988 964 863 ÷ 2 = 34 494 482 431 + 1;
  • 34 494 482 431 ÷ 2 = 17 247 241 215 + 1;
  • 17 247 241 215 ÷ 2 = 8 623 620 607 + 1;
  • 8 623 620 607 ÷ 2 = 4 311 810 303 + 1;
  • 4 311 810 303 ÷ 2 = 2 155 905 151 + 1;
  • 2 155 905 151 ÷ 2 = 1 077 952 575 + 1;
  • 1 077 952 575 ÷ 2 = 538 976 287 + 1;
  • 538 976 287 ÷ 2 = 269 488 143 + 1;
  • 269 488 143 ÷ 2 = 134 744 071 + 1;
  • 134 744 071 ÷ 2 = 67 372 035 + 1;
  • 67 372 035 ÷ 2 = 33 686 017 + 1;
  • 33 686 017 ÷ 2 = 16 843 008 + 1;
  • 16 843 008 ÷ 2 = 8 421 504 + 0;
  • 8 421 504 ÷ 2 = 4 210 752 + 0;
  • 4 210 752 ÷ 2 = 2 105 376 + 0;
  • 2 105 376 ÷ 2 = 1 052 688 + 0;
  • 1 052 688 ÷ 2 = 526 344 + 0;
  • 526 344 ÷ 2 = 263 172 + 0;
  • 263 172 ÷ 2 = 131 586 + 0;
  • 131 586 ÷ 2 = 65 793 + 0;
  • 65 793 ÷ 2 = 32 896 + 1;
  • 32 896 ÷ 2 = 16 448 + 0;
  • 16 448 ÷ 2 = 8 224 + 0;
  • 8 224 ÷ 2 = 4 112 + 0;
  • 4 112 ÷ 2 = 2 056 + 0;
  • 2 056 ÷ 2 = 1 028 + 0;
  • 1 028 ÷ 2 = 514 + 0;
  • 514 ÷ 2 = 257 + 0;
  • 257 ÷ 2 = 128 + 1;
  • 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;

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

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

36 170 086 410 616 699(10) = 1000 0000 1000 0000 1000 0000 0111 1111 1111 1111 1111 1111 0111 1011(2)


4. Determine the signed binary number bit length:

  • The base 2 number's actual length, in bits: 56.

  • 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, 56,

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:


36 170 086 410 616 699(10) = 0000 0000 1000 0000 1000 0000 1000 0000 0111 1111 1111 1111 1111 1111 0111 1011

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...


-36 170 086 410 616 699(10) Base 10 integer number converted and written as a signed binary code (in base 2):

-36 170 086 410 616 699(10) = 1000 0000 1000 0000 1000 0000 1000 0000 0111 1111 1111 1111 1111 1111 0111 1011

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