Signed: Integer ↗ Binary: -4 611 686 018 427 387 915 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 -4 611 686 018 427 387 915(10)
converted and written as a signed binary (base 2) = ?

1. Start with the positive version of the number:

|-4 611 686 018 427 387 915| = 4 611 686 018 427 387 915

2. 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;
  • 4 611 686 018 427 387 915 ÷ 2 = 2 305 843 009 213 693 957 + 1;
  • 2 305 843 009 213 693 957 ÷ 2 = 1 152 921 504 606 846 978 + 1;
  • 1 152 921 504 606 846 978 ÷ 2 = 576 460 752 303 423 489 + 0;
  • 576 460 752 303 423 489 ÷ 2 = 288 230 376 151 711 744 + 1;
  • 288 230 376 151 711 744 ÷ 2 = 144 115 188 075 855 872 + 0;
  • 144 115 188 075 855 872 ÷ 2 = 72 057 594 037 927 936 + 0;
  • 72 057 594 037 927 936 ÷ 2 = 36 028 797 018 963 968 + 0;
  • 36 028 797 018 963 968 ÷ 2 = 18 014 398 509 481 984 + 0;
  • 18 014 398 509 481 984 ÷ 2 = 9 007 199 254 740 992 + 0;
  • 9 007 199 254 740 992 ÷ 2 = 4 503 599 627 370 496 + 0;
  • 4 503 599 627 370 496 ÷ 2 = 2 251 799 813 685 248 + 0;
  • 2 251 799 813 685 248 ÷ 2 = 1 125 899 906 842 624 + 0;
  • 1 125 899 906 842 624 ÷ 2 = 562 949 953 421 312 + 0;
  • 562 949 953 421 312 ÷ 2 = 281 474 976 710 656 + 0;
  • 281 474 976 710 656 ÷ 2 = 140 737 488 355 328 + 0;
  • 140 737 488 355 328 ÷ 2 = 70 368 744 177 664 + 0;
  • 70 368 744 177 664 ÷ 2 = 35 184 372 088 832 + 0;
  • 35 184 372 088 832 ÷ 2 = 17 592 186 044 416 + 0;
  • 17 592 186 044 416 ÷ 2 = 8 796 093 022 208 + 0;
  • 8 796 093 022 208 ÷ 2 = 4 398 046 511 104 + 0;
  • 4 398 046 511 104 ÷ 2 = 2 199 023 255 552 + 0;
  • 2 199 023 255 552 ÷ 2 = 1 099 511 627 776 + 0;
  • 1 099 511 627 776 ÷ 2 = 549 755 813 888 + 0;
  • 549 755 813 888 ÷ 2 = 274 877 906 944 + 0;
  • 274 877 906 944 ÷ 2 = 137 438 953 472 + 0;
  • 137 438 953 472 ÷ 2 = 68 719 476 736 + 0;
  • 68 719 476 736 ÷ 2 = 34 359 738 368 + 0;
  • 34 359 738 368 ÷ 2 = 17 179 869 184 + 0;
  • 17 179 869 184 ÷ 2 = 8 589 934 592 + 0;
  • 8 589 934 592 ÷ 2 = 4 294 967 296 + 0;
  • 4 294 967 296 ÷ 2 = 2 147 483 648 + 0;
  • 2 147 483 648 ÷ 2 = 1 073 741 824 + 0;
  • 1 073 741 824 ÷ 2 = 536 870 912 + 0;
  • 536 870 912 ÷ 2 = 268 435 456 + 0;
  • 268 435 456 ÷ 2 = 134 217 728 + 0;
  • 134 217 728 ÷ 2 = 67 108 864 + 0;
  • 67 108 864 ÷ 2 = 33 554 432 + 0;
  • 33 554 432 ÷ 2 = 16 777 216 + 0;
  • 16 777 216 ÷ 2 = 8 388 608 + 0;
  • 8 388 608 ÷ 2 = 4 194 304 + 0;
  • 4 194 304 ÷ 2 = 2 097 152 + 0;
  • 2 097 152 ÷ 2 = 1 048 576 + 0;
  • 1 048 576 ÷ 2 = 524 288 + 0;
  • 524 288 ÷ 2 = 262 144 + 0;
  • 262 144 ÷ 2 = 131 072 + 0;
  • 131 072 ÷ 2 = 65 536 + 0;
  • 65 536 ÷ 2 = 32 768 + 0;
  • 32 768 ÷ 2 = 16 384 + 0;
  • 16 384 ÷ 2 = 8 192 + 0;
  • 8 192 ÷ 2 = 4 096 + 0;
  • 4 096 ÷ 2 = 2 048 + 0;
  • 2 048 ÷ 2 = 1 024 + 0;
  • 1 024 ÷ 2 = 512 + 0;
  • 512 ÷ 2 = 256 + 0;
  • 256 ÷ 2 = 128 + 0;
  • 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.


4 611 686 018 427 387 915(10) = 100 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 1011(2)


4. Determine the signed binary number bit length:

The base 2 number's actual length, in bits: 63.

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, 63,

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:


4 611 686 018 427 387 915(10) = 0100 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 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...


Number -4 611 686 018 427 387 915(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):

-4 611 686 018 427 387 915(10) = 1100 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 1011

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

More operations on signed integer numbers:

» Signed integer number -4 611 686 018 427 387 916 converted from decimal system (from base 10) and written as a signed binary (in base 2) = ?

» Signed integer number -4 611 686 018 427 387 914 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