Convert 202 200 701 709 538 541 to a Signed Binary (Base 2)

How to convert 202 200 701 709 538 541(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 202 200 701 709 538 541 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;
  • 202 200 701 709 538 541 ÷ 2 = 101 100 350 854 769 270 + 1;
  • 101 100 350 854 769 270 ÷ 2 = 50 550 175 427 384 635 + 0;
  • 50 550 175 427 384 635 ÷ 2 = 25 275 087 713 692 317 + 1;
  • 25 275 087 713 692 317 ÷ 2 = 12 637 543 856 846 158 + 1;
  • 12 637 543 856 846 158 ÷ 2 = 6 318 771 928 423 079 + 0;
  • 6 318 771 928 423 079 ÷ 2 = 3 159 385 964 211 539 + 1;
  • 3 159 385 964 211 539 ÷ 2 = 1 579 692 982 105 769 + 1;
  • 1 579 692 982 105 769 ÷ 2 = 789 846 491 052 884 + 1;
  • 789 846 491 052 884 ÷ 2 = 394 923 245 526 442 + 0;
  • 394 923 245 526 442 ÷ 2 = 197 461 622 763 221 + 0;
  • 197 461 622 763 221 ÷ 2 = 98 730 811 381 610 + 1;
  • 98 730 811 381 610 ÷ 2 = 49 365 405 690 805 + 0;
  • 49 365 405 690 805 ÷ 2 = 24 682 702 845 402 + 1;
  • 24 682 702 845 402 ÷ 2 = 12 341 351 422 701 + 0;
  • 12 341 351 422 701 ÷ 2 = 6 170 675 711 350 + 1;
  • 6 170 675 711 350 ÷ 2 = 3 085 337 855 675 + 0;
  • 3 085 337 855 675 ÷ 2 = 1 542 668 927 837 + 1;
  • 1 542 668 927 837 ÷ 2 = 771 334 463 918 + 1;
  • 771 334 463 918 ÷ 2 = 385 667 231 959 + 0;
  • 385 667 231 959 ÷ 2 = 192 833 615 979 + 1;
  • 192 833 615 979 ÷ 2 = 96 416 807 989 + 1;
  • 96 416 807 989 ÷ 2 = 48 208 403 994 + 1;
  • 48 208 403 994 ÷ 2 = 24 104 201 997 + 0;
  • 24 104 201 997 ÷ 2 = 12 052 100 998 + 1;
  • 12 052 100 998 ÷ 2 = 6 026 050 499 + 0;
  • 6 026 050 499 ÷ 2 = 3 013 025 249 + 1;
  • 3 013 025 249 ÷ 2 = 1 506 512 624 + 1;
  • 1 506 512 624 ÷ 2 = 753 256 312 + 0;
  • 753 256 312 ÷ 2 = 376 628 156 + 0;
  • 376 628 156 ÷ 2 = 188 314 078 + 0;
  • 188 314 078 ÷ 2 = 94 157 039 + 0;
  • 94 157 039 ÷ 2 = 47 078 519 + 1;
  • 47 078 519 ÷ 2 = 23 539 259 + 1;
  • 23 539 259 ÷ 2 = 11 769 629 + 1;
  • 11 769 629 ÷ 2 = 5 884 814 + 1;
  • 5 884 814 ÷ 2 = 2 942 407 + 0;
  • 2 942 407 ÷ 2 = 1 471 203 + 1;
  • 1 471 203 ÷ 2 = 735 601 + 1;
  • 735 601 ÷ 2 = 367 800 + 1;
  • 367 800 ÷ 2 = 183 900 + 0;
  • 183 900 ÷ 2 = 91 950 + 0;
  • 91 950 ÷ 2 = 45 975 + 0;
  • 45 975 ÷ 2 = 22 987 + 1;
  • 22 987 ÷ 2 = 11 493 + 1;
  • 11 493 ÷ 2 = 5 746 + 1;
  • 5 746 ÷ 2 = 2 873 + 0;
  • 2 873 ÷ 2 = 1 436 + 1;
  • 1 436 ÷ 2 = 718 + 0;
  • 718 ÷ 2 = 359 + 0;
  • 359 ÷ 2 = 179 + 1;
  • 179 ÷ 2 = 89 + 1;
  • 89 ÷ 2 = 44 + 1;
  • 44 ÷ 2 = 22 + 0;
  • 22 ÷ 2 = 11 + 0;
  • 11 ÷ 2 = 5 + 1;
  • 5 ÷ 2 = 2 + 1;
  • 2 ÷ 2 = 1 + 0;
  • 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.

202 200 701 709 538 541(10) = 10 1100 1110 0101 1100 0111 0111 1000 0110 1011 1011 0101 0100 1110 1101(2)


3. Determine the signed binary number bit length:

  • The base 2 number's actual length, in bits: 58.

  • 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, 58,

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:


202 200 701 709 538 541(10) Base 10 integer number converted and written as a signed binary code (in base 2):

202 200 701 709 538 541(10) = 0000 0010 1100 1110 0101 1100 0111 0111 1000 0110 1011 1011 0101 0100 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