Convert -432 345 572 951 720 965 to a Signed Binary (Base 2)

How to convert -432 345 572 951 720 965(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 -432 345 572 951 720 965 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:

|-432 345 572 951 720 965| = 432 345 572 951 720 965

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;
  • 432 345 572 951 720 965 ÷ 2 = 216 172 786 475 860 482 + 1;
  • 216 172 786 475 860 482 ÷ 2 = 108 086 393 237 930 241 + 0;
  • 108 086 393 237 930 241 ÷ 2 = 54 043 196 618 965 120 + 1;
  • 54 043 196 618 965 120 ÷ 2 = 27 021 598 309 482 560 + 0;
  • 27 021 598 309 482 560 ÷ 2 = 13 510 799 154 741 280 + 0;
  • 13 510 799 154 741 280 ÷ 2 = 6 755 399 577 370 640 + 0;
  • 6 755 399 577 370 640 ÷ 2 = 3 377 699 788 685 320 + 0;
  • 3 377 699 788 685 320 ÷ 2 = 1 688 849 894 342 660 + 0;
  • 1 688 849 894 342 660 ÷ 2 = 844 424 947 171 330 + 0;
  • 844 424 947 171 330 ÷ 2 = 422 212 473 585 665 + 0;
  • 422 212 473 585 665 ÷ 2 = 211 106 236 792 832 + 1;
  • 211 106 236 792 832 ÷ 2 = 105 553 118 396 416 + 0;
  • 105 553 118 396 416 ÷ 2 = 52 776 559 198 208 + 0;
  • 52 776 559 198 208 ÷ 2 = 26 388 279 599 104 + 0;
  • 26 388 279 599 104 ÷ 2 = 13 194 139 799 552 + 0;
  • 13 194 139 799 552 ÷ 2 = 6 597 069 899 776 + 0;
  • 6 597 069 899 776 ÷ 2 = 3 298 534 949 888 + 0;
  • 3 298 534 949 888 ÷ 2 = 1 649 267 474 944 + 0;
  • 1 649 267 474 944 ÷ 2 = 824 633 737 472 + 0;
  • 824 633 737 472 ÷ 2 = 412 316 868 736 + 0;
  • 412 316 868 736 ÷ 2 = 206 158 434 368 + 0;
  • 206 158 434 368 ÷ 2 = 103 079 217 184 + 0;
  • 103 079 217 184 ÷ 2 = 51 539 608 592 + 0;
  • 51 539 608 592 ÷ 2 = 25 769 804 296 + 0;
  • 25 769 804 296 ÷ 2 = 12 884 902 148 + 0;
  • 12 884 902 148 ÷ 2 = 6 442 451 074 + 0;
  • 6 442 451 074 ÷ 2 = 3 221 225 537 + 0;
  • 3 221 225 537 ÷ 2 = 1 610 612 768 + 1;
  • 1 610 612 768 ÷ 2 = 805 306 384 + 0;
  • 805 306 384 ÷ 2 = 402 653 192 + 0;
  • 402 653 192 ÷ 2 = 201 326 596 + 0;
  • 201 326 596 ÷ 2 = 100 663 298 + 0;
  • 100 663 298 ÷ 2 = 50 331 649 + 0;
  • 50 331 649 ÷ 2 = 25 165 824 + 1;
  • 25 165 824 ÷ 2 = 12 582 912 + 0;
  • 12 582 912 ÷ 2 = 6 291 456 + 0;
  • 6 291 456 ÷ 2 = 3 145 728 + 0;
  • 3 145 728 ÷ 2 = 1 572 864 + 0;
  • 1 572 864 ÷ 2 = 786 432 + 0;
  • 786 432 ÷ 2 = 393 216 + 0;
  • 393 216 ÷ 2 = 196 608 + 0;
  • 196 608 ÷ 2 = 98 304 + 0;
  • 98 304 ÷ 2 = 49 152 + 0;
  • 49 152 ÷ 2 = 24 576 + 0;
  • 24 576 ÷ 2 = 12 288 + 0;
  • 12 288 ÷ 2 = 6 144 + 0;
  • 6 144 ÷ 2 = 3 072 + 0;
  • 3 072 ÷ 2 = 1 536 + 0;
  • 1 536 ÷ 2 = 768 + 0;
  • 768 ÷ 2 = 384 + 0;
  • 384 ÷ 2 = 192 + 0;
  • 192 ÷ 2 = 96 + 0;
  • 96 ÷ 2 = 48 + 0;
  • 48 ÷ 2 = 24 + 0;
  • 24 ÷ 2 = 12 + 0;
  • 12 ÷ 2 = 6 + 0;
  • 6 ÷ 2 = 3 + 0;
  • 3 ÷ 2 = 1 + 1;
  • 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.

432 345 572 951 720 965(10) = 110 0000 0000 0000 0000 0000 0010 0000 1000 0000 0000 0000 0100 0000 0101(2)


4. Determine the signed binary number bit length:

  • The base 2 number's actual length, in bits: 59.

  • 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, 59,

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:


432 345 572 951 720 965(10) = 0000 0110 0000 0000 0000 0000 0000 0010 0000 1000 0000 0000 0000 0100 0000 0101

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...


-432 345 572 951 720 965(10) Base 10 integer number converted and written as a signed binary code (in base 2):

-432 345 572 951 720 965(10) = 1000 0110 0000 0000 0000 0000 0000 0010 0000 1000 0000 0000 0000 0100 0000 0101

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