Convert 271 362 650 271 981 to a Signed Binary (Base 2)

How to convert 271 362 650 271 981(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 271 362 650 271 981 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. 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;
  • 271 362 650 271 981 ÷ 2 = 135 681 325 135 990 + 1;
  • 135 681 325 135 990 ÷ 2 = 67 840 662 567 995 + 0;
  • 67 840 662 567 995 ÷ 2 = 33 920 331 283 997 + 1;
  • 33 920 331 283 997 ÷ 2 = 16 960 165 641 998 + 1;
  • 16 960 165 641 998 ÷ 2 = 8 480 082 820 999 + 0;
  • 8 480 082 820 999 ÷ 2 = 4 240 041 410 499 + 1;
  • 4 240 041 410 499 ÷ 2 = 2 120 020 705 249 + 1;
  • 2 120 020 705 249 ÷ 2 = 1 060 010 352 624 + 1;
  • 1 060 010 352 624 ÷ 2 = 530 005 176 312 + 0;
  • 530 005 176 312 ÷ 2 = 265 002 588 156 + 0;
  • 265 002 588 156 ÷ 2 = 132 501 294 078 + 0;
  • 132 501 294 078 ÷ 2 = 66 250 647 039 + 0;
  • 66 250 647 039 ÷ 2 = 33 125 323 519 + 1;
  • 33 125 323 519 ÷ 2 = 16 562 661 759 + 1;
  • 16 562 661 759 ÷ 2 = 8 281 330 879 + 1;
  • 8 281 330 879 ÷ 2 = 4 140 665 439 + 1;
  • 4 140 665 439 ÷ 2 = 2 070 332 719 + 1;
  • 2 070 332 719 ÷ 2 = 1 035 166 359 + 1;
  • 1 035 166 359 ÷ 2 = 517 583 179 + 1;
  • 517 583 179 ÷ 2 = 258 791 589 + 1;
  • 258 791 589 ÷ 2 = 129 395 794 + 1;
  • 129 395 794 ÷ 2 = 64 697 897 + 0;
  • 64 697 897 ÷ 2 = 32 348 948 + 1;
  • 32 348 948 ÷ 2 = 16 174 474 + 0;
  • 16 174 474 ÷ 2 = 8 087 237 + 0;
  • 8 087 237 ÷ 2 = 4 043 618 + 1;
  • 4 043 618 ÷ 2 = 2 021 809 + 0;
  • 2 021 809 ÷ 2 = 1 010 904 + 1;
  • 1 010 904 ÷ 2 = 505 452 + 0;
  • 505 452 ÷ 2 = 252 726 + 0;
  • 252 726 ÷ 2 = 126 363 + 0;
  • 126 363 ÷ 2 = 63 181 + 1;
  • 63 181 ÷ 2 = 31 590 + 1;
  • 31 590 ÷ 2 = 15 795 + 0;
  • 15 795 ÷ 2 = 7 897 + 1;
  • 7 897 ÷ 2 = 3 948 + 1;
  • 3 948 ÷ 2 = 1 974 + 0;
  • 1 974 ÷ 2 = 987 + 0;
  • 987 ÷ 2 = 493 + 1;
  • 493 ÷ 2 = 246 + 1;
  • 246 ÷ 2 = 123 + 0;
  • 123 ÷ 2 = 61 + 1;
  • 61 ÷ 2 = 30 + 1;
  • 30 ÷ 2 = 15 + 0;
  • 15 ÷ 2 = 7 + 1;
  • 7 ÷ 2 = 3 + 1;
  • 3 ÷ 2 = 1 + 1;
  • 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.

271 362 650 271 981(10) = 1111 0110 1100 1101 1000 1010 0101 1111 1111 0000 1110 1101(2)


3. Determine the signed binary number bit length:

  • The base 2 number's actual length, in bits: 48.

  • 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, 48,

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:


271 362 650 271 981(10) Base 10 integer number converted and written as a signed binary code (in base 2):

271 362 650 271 981(10) = 0000 0000 0000 0000 1111 0110 1100 1101 1000 1010 0101 1111 1111 0000 1110 1101

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