Convert -62 135 596 799 953 to a Signed Binary (Base 2)

How to convert -62 135 596 799 953(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 -62 135 596 799 953 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:

|-62 135 596 799 953| = 62 135 596 799 953

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;
  • 62 135 596 799 953 ÷ 2 = 31 067 798 399 976 + 1;
  • 31 067 798 399 976 ÷ 2 = 15 533 899 199 988 + 0;
  • 15 533 899 199 988 ÷ 2 = 7 766 949 599 994 + 0;
  • 7 766 949 599 994 ÷ 2 = 3 883 474 799 997 + 0;
  • 3 883 474 799 997 ÷ 2 = 1 941 737 399 998 + 1;
  • 1 941 737 399 998 ÷ 2 = 970 868 699 999 + 0;
  • 970 868 699 999 ÷ 2 = 485 434 349 999 + 1;
  • 485 434 349 999 ÷ 2 = 242 717 174 999 + 1;
  • 242 717 174 999 ÷ 2 = 121 358 587 499 + 1;
  • 121 358 587 499 ÷ 2 = 60 679 293 749 + 1;
  • 60 679 293 749 ÷ 2 = 30 339 646 874 + 1;
  • 30 339 646 874 ÷ 2 = 15 169 823 437 + 0;
  • 15 169 823 437 ÷ 2 = 7 584 911 718 + 1;
  • 7 584 911 718 ÷ 2 = 3 792 455 859 + 0;
  • 3 792 455 859 ÷ 2 = 1 896 227 929 + 1;
  • 1 896 227 929 ÷ 2 = 948 113 964 + 1;
  • 948 113 964 ÷ 2 = 474 056 982 + 0;
  • 474 056 982 ÷ 2 = 237 028 491 + 0;
  • 237 028 491 ÷ 2 = 118 514 245 + 1;
  • 118 514 245 ÷ 2 = 59 257 122 + 1;
  • 59 257 122 ÷ 2 = 29 628 561 + 0;
  • 29 628 561 ÷ 2 = 14 814 280 + 1;
  • 14 814 280 ÷ 2 = 7 407 140 + 0;
  • 7 407 140 ÷ 2 = 3 703 570 + 0;
  • 3 703 570 ÷ 2 = 1 851 785 + 0;
  • 1 851 785 ÷ 2 = 925 892 + 1;
  • 925 892 ÷ 2 = 462 946 + 0;
  • 462 946 ÷ 2 = 231 473 + 0;
  • 231 473 ÷ 2 = 115 736 + 1;
  • 115 736 ÷ 2 = 57 868 + 0;
  • 57 868 ÷ 2 = 28 934 + 0;
  • 28 934 ÷ 2 = 14 467 + 0;
  • 14 467 ÷ 2 = 7 233 + 1;
  • 7 233 ÷ 2 = 3 616 + 1;
  • 3 616 ÷ 2 = 1 808 + 0;
  • 1 808 ÷ 2 = 904 + 0;
  • 904 ÷ 2 = 452 + 0;
  • 452 ÷ 2 = 226 + 0;
  • 226 ÷ 2 = 113 + 0;
  • 113 ÷ 2 = 56 + 1;
  • 56 ÷ 2 = 28 + 0;
  • 28 ÷ 2 = 14 + 0;
  • 14 ÷ 2 = 7 + 0;
  • 7 ÷ 2 = 3 + 1;
  • 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.

62 135 596 799 953(10) = 11 1000 1000 0011 0001 0010 0010 1100 1101 0111 1101 0001(2)


4. Determine the signed binary number bit length:

  • The base 2 number's actual length, in bits: 46.

  • 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, 46,

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:


62 135 596 799 953(10) = 0000 0000 0000 0000 0011 1000 1000 0011 0001 0010 0010 1100 1101 0111 1101 0001

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...


-62 135 596 799 953(10) Base 10 integer number converted and written as a signed binary code (in base 2):

-62 135 596 799 953(10) = 1000 0000 0000 0000 0011 1000 1000 0011 0001 0010 0010 1100 1101 0111 1101 0001

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