Convert 432 345 572 951 719 862 to a Signed Binary (Base 2)

How to convert 432 345 572 951 719 862(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 432 345 572 951 719 862 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;
  • 432 345 572 951 719 862 ÷ 2 = 216 172 786 475 859 931 + 0;
  • 216 172 786 475 859 931 ÷ 2 = 108 086 393 237 929 965 + 1;
  • 108 086 393 237 929 965 ÷ 2 = 54 043 196 618 964 982 + 1;
  • 54 043 196 618 964 982 ÷ 2 = 27 021 598 309 482 491 + 0;
  • 27 021 598 309 482 491 ÷ 2 = 13 510 799 154 741 245 + 1;
  • 13 510 799 154 741 245 ÷ 2 = 6 755 399 577 370 622 + 1;
  • 6 755 399 577 370 622 ÷ 2 = 3 377 699 788 685 311 + 0;
  • 3 377 699 788 685 311 ÷ 2 = 1 688 849 894 342 655 + 1;
  • 1 688 849 894 342 655 ÷ 2 = 844 424 947 171 327 + 1;
  • 844 424 947 171 327 ÷ 2 = 422 212 473 585 663 + 1;
  • 422 212 473 585 663 ÷ 2 = 211 106 236 792 831 + 1;
  • 211 106 236 792 831 ÷ 2 = 105 553 118 396 415 + 1;
  • 105 553 118 396 415 ÷ 2 = 52 776 559 198 207 + 1;
  • 52 776 559 198 207 ÷ 2 = 26 388 279 599 103 + 1;
  • 26 388 279 599 103 ÷ 2 = 13 194 139 799 551 + 1;
  • 13 194 139 799 551 ÷ 2 = 6 597 069 899 775 + 1;
  • 6 597 069 899 775 ÷ 2 = 3 298 534 949 887 + 1;
  • 3 298 534 949 887 ÷ 2 = 1 649 267 474 943 + 1;
  • 1 649 267 474 943 ÷ 2 = 824 633 737 471 + 1;
  • 824 633 737 471 ÷ 2 = 412 316 868 735 + 1;
  • 412 316 868 735 ÷ 2 = 206 158 434 367 + 1;
  • 206 158 434 367 ÷ 2 = 103 079 217 183 + 1;
  • 103 079 217 183 ÷ 2 = 51 539 608 591 + 1;
  • 51 539 608 591 ÷ 2 = 25 769 804 295 + 1;
  • 25 769 804 295 ÷ 2 = 12 884 902 147 + 1;
  • 12 884 902 147 ÷ 2 = 6 442 451 073 + 1;
  • 6 442 451 073 ÷ 2 = 3 221 225 536 + 1;
  • 3 221 225 536 ÷ 2 = 1 610 612 768 + 0;
  • 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;

2. Construct the base 2 representation of the positive number:

Take all the remainders starting from the bottom of the list constructed above.

432 345 572 951 719 862(10) = 110 0000 0000 0000 0000 0000 0010 0000 0111 1111 1111 1111 1111 1011 0110(2)


3. 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.


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:


432 345 572 951 719 862(10) Base 10 integer number converted and written as a signed binary code (in base 2):

432 345 572 951 719 862(10) = 0000 0110 0000 0000 0000 0000 0000 0010 0000 0111 1111 1111 1111 1111 1011 0110

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