Signed: Integer ↗ Binary: 288 230 376 151 711 720 Convert the Integer Number to a Signed Binary. Converting and Writing the Base Ten Decimal System Signed Integer as Binary Code (Written in Base Two)

Signed integer number 288 230 376 151 711 720(10)
converted and written as a signed binary (base 2) = ?

1. Divide the number repeatedly by 2:

Keep track of each remainder.

We stop when we get a quotient that is equal to zero.


  • division = quotient + remainder;
  • 288 230 376 151 711 720 ÷ 2 = 144 115 188 075 855 860 + 0;
  • 144 115 188 075 855 860 ÷ 2 = 72 057 594 037 927 930 + 0;
  • 72 057 594 037 927 930 ÷ 2 = 36 028 797 018 963 965 + 0;
  • 36 028 797 018 963 965 ÷ 2 = 18 014 398 509 481 982 + 1;
  • 18 014 398 509 481 982 ÷ 2 = 9 007 199 254 740 991 + 0;
  • 9 007 199 254 740 991 ÷ 2 = 4 503 599 627 370 495 + 1;
  • 4 503 599 627 370 495 ÷ 2 = 2 251 799 813 685 247 + 1;
  • 2 251 799 813 685 247 ÷ 2 = 1 125 899 906 842 623 + 1;
  • 1 125 899 906 842 623 ÷ 2 = 562 949 953 421 311 + 1;
  • 562 949 953 421 311 ÷ 2 = 281 474 976 710 655 + 1;
  • 281 474 976 710 655 ÷ 2 = 140 737 488 355 327 + 1;
  • 140 737 488 355 327 ÷ 2 = 70 368 744 177 663 + 1;
  • 70 368 744 177 663 ÷ 2 = 35 184 372 088 831 + 1;
  • 35 184 372 088 831 ÷ 2 = 17 592 186 044 415 + 1;
  • 17 592 186 044 415 ÷ 2 = 8 796 093 022 207 + 1;
  • 8 796 093 022 207 ÷ 2 = 4 398 046 511 103 + 1;
  • 4 398 046 511 103 ÷ 2 = 2 199 023 255 551 + 1;
  • 2 199 023 255 551 ÷ 2 = 1 099 511 627 775 + 1;
  • 1 099 511 627 775 ÷ 2 = 549 755 813 887 + 1;
  • 549 755 813 887 ÷ 2 = 274 877 906 943 + 1;
  • 274 877 906 943 ÷ 2 = 137 438 953 471 + 1;
  • 137 438 953 471 ÷ 2 = 68 719 476 735 + 1;
  • 68 719 476 735 ÷ 2 = 34 359 738 367 + 1;
  • 34 359 738 367 ÷ 2 = 17 179 869 183 + 1;
  • 17 179 869 183 ÷ 2 = 8 589 934 591 + 1;
  • 8 589 934 591 ÷ 2 = 4 294 967 295 + 1;
  • 4 294 967 295 ÷ 2 = 2 147 483 647 + 1;
  • 2 147 483 647 ÷ 2 = 1 073 741 823 + 1;
  • 1 073 741 823 ÷ 2 = 536 870 911 + 1;
  • 536 870 911 ÷ 2 = 268 435 455 + 1;
  • 268 435 455 ÷ 2 = 134 217 727 + 1;
  • 134 217 727 ÷ 2 = 67 108 863 + 1;
  • 67 108 863 ÷ 2 = 33 554 431 + 1;
  • 33 554 431 ÷ 2 = 16 777 215 + 1;
  • 16 777 215 ÷ 2 = 8 388 607 + 1;
  • 8 388 607 ÷ 2 = 4 194 303 + 1;
  • 4 194 303 ÷ 2 = 2 097 151 + 1;
  • 2 097 151 ÷ 2 = 1 048 575 + 1;
  • 1 048 575 ÷ 2 = 524 287 + 1;
  • 524 287 ÷ 2 = 262 143 + 1;
  • 262 143 ÷ 2 = 131 071 + 1;
  • 131 071 ÷ 2 = 65 535 + 1;
  • 65 535 ÷ 2 = 32 767 + 1;
  • 32 767 ÷ 2 = 16 383 + 1;
  • 16 383 ÷ 2 = 8 191 + 1;
  • 8 191 ÷ 2 = 4 095 + 1;
  • 4 095 ÷ 2 = 2 047 + 1;
  • 2 047 ÷ 2 = 1 023 + 1;
  • 1 023 ÷ 2 = 511 + 1;
  • 511 ÷ 2 = 255 + 1;
  • 255 ÷ 2 = 127 + 1;
  • 127 ÷ 2 = 63 + 1;
  • 63 ÷ 2 = 31 + 1;
  • 31 ÷ 2 = 15 + 1;
  • 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.


288 230 376 151 711 720(10) = 11 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1110 1000(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:


Number 288 230 376 151 711 720(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):

288 230 376 151 711 720(10) = 0000 0011 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1110 1000

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

More operations on signed integer numbers:

» Signed integer number 288 230 376 151 711 719 converted from decimal system (from base 10) and written as a signed binary (in base 2) = ?

» Signed integer number 288 230 376 151 711 721 converted from decimal system (from base 10) and written as a signed binary (in base 2) = ?

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How to convert signed integers from decimal system 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