Convert -80 449 340 000 342 to a Signed Binary (Base 2)

How to convert -80 449 340 000 342(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 -80 449 340 000 342 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:

|-80 449 340 000 342| = 80 449 340 000 342

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;
  • 80 449 340 000 342 ÷ 2 = 40 224 670 000 171 + 0;
  • 40 224 670 000 171 ÷ 2 = 20 112 335 000 085 + 1;
  • 20 112 335 000 085 ÷ 2 = 10 056 167 500 042 + 1;
  • 10 056 167 500 042 ÷ 2 = 5 028 083 750 021 + 0;
  • 5 028 083 750 021 ÷ 2 = 2 514 041 875 010 + 1;
  • 2 514 041 875 010 ÷ 2 = 1 257 020 937 505 + 0;
  • 1 257 020 937 505 ÷ 2 = 628 510 468 752 + 1;
  • 628 510 468 752 ÷ 2 = 314 255 234 376 + 0;
  • 314 255 234 376 ÷ 2 = 157 127 617 188 + 0;
  • 157 127 617 188 ÷ 2 = 78 563 808 594 + 0;
  • 78 563 808 594 ÷ 2 = 39 281 904 297 + 0;
  • 39 281 904 297 ÷ 2 = 19 640 952 148 + 1;
  • 19 640 952 148 ÷ 2 = 9 820 476 074 + 0;
  • 9 820 476 074 ÷ 2 = 4 910 238 037 + 0;
  • 4 910 238 037 ÷ 2 = 2 455 119 018 + 1;
  • 2 455 119 018 ÷ 2 = 1 227 559 509 + 0;
  • 1 227 559 509 ÷ 2 = 613 779 754 + 1;
  • 613 779 754 ÷ 2 = 306 889 877 + 0;
  • 306 889 877 ÷ 2 = 153 444 938 + 1;
  • 153 444 938 ÷ 2 = 76 722 469 + 0;
  • 76 722 469 ÷ 2 = 38 361 234 + 1;
  • 38 361 234 ÷ 2 = 19 180 617 + 0;
  • 19 180 617 ÷ 2 = 9 590 308 + 1;
  • 9 590 308 ÷ 2 = 4 795 154 + 0;
  • 4 795 154 ÷ 2 = 2 397 577 + 0;
  • 2 397 577 ÷ 2 = 1 198 788 + 1;
  • 1 198 788 ÷ 2 = 599 394 + 0;
  • 599 394 ÷ 2 = 299 697 + 0;
  • 299 697 ÷ 2 = 149 848 + 1;
  • 149 848 ÷ 2 = 74 924 + 0;
  • 74 924 ÷ 2 = 37 462 + 0;
  • 37 462 ÷ 2 = 18 731 + 0;
  • 18 731 ÷ 2 = 9 365 + 1;
  • 9 365 ÷ 2 = 4 682 + 1;
  • 4 682 ÷ 2 = 2 341 + 0;
  • 2 341 ÷ 2 = 1 170 + 1;
  • 1 170 ÷ 2 = 585 + 0;
  • 585 ÷ 2 = 292 + 1;
  • 292 ÷ 2 = 146 + 0;
  • 146 ÷ 2 = 73 + 0;
  • 73 ÷ 2 = 36 + 1;
  • 36 ÷ 2 = 18 + 0;
  • 18 ÷ 2 = 9 + 0;
  • 9 ÷ 2 = 4 + 1;
  • 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.

80 449 340 000 342(10) = 100 1001 0010 1011 0001 0010 0101 0101 0100 1000 0101 0110(2)


4. Determine the signed binary number bit length:

  • The base 2 number's actual length, in bits: 47.

  • 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, 47,

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:


80 449 340 000 342(10) = 0000 0000 0000 0000 0100 1001 0010 1011 0001 0010 0101 0101 0100 1000 0101 0110

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...


-80 449 340 000 342(10) Base 10 integer number converted and written as a signed binary code (in base 2):

-80 449 340 000 342(10) = 1000 0000 0000 0000 0100 1001 0010 1011 0001 0010 0101 0101 0100 1000 0101 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