Convert -1 336 147 191 563 544 666 to a Signed Binary (Base 2)

How to convert -1 336 147 191 563 544 666(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 -1 336 147 191 563 544 666 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:

|-1 336 147 191 563 544 666| = 1 336 147 191 563 544 666

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;
  • 1 336 147 191 563 544 666 ÷ 2 = 668 073 595 781 772 333 + 0;
  • 668 073 595 781 772 333 ÷ 2 = 334 036 797 890 886 166 + 1;
  • 334 036 797 890 886 166 ÷ 2 = 167 018 398 945 443 083 + 0;
  • 167 018 398 945 443 083 ÷ 2 = 83 509 199 472 721 541 + 1;
  • 83 509 199 472 721 541 ÷ 2 = 41 754 599 736 360 770 + 1;
  • 41 754 599 736 360 770 ÷ 2 = 20 877 299 868 180 385 + 0;
  • 20 877 299 868 180 385 ÷ 2 = 10 438 649 934 090 192 + 1;
  • 10 438 649 934 090 192 ÷ 2 = 5 219 324 967 045 096 + 0;
  • 5 219 324 967 045 096 ÷ 2 = 2 609 662 483 522 548 + 0;
  • 2 609 662 483 522 548 ÷ 2 = 1 304 831 241 761 274 + 0;
  • 1 304 831 241 761 274 ÷ 2 = 652 415 620 880 637 + 0;
  • 652 415 620 880 637 ÷ 2 = 326 207 810 440 318 + 1;
  • 326 207 810 440 318 ÷ 2 = 163 103 905 220 159 + 0;
  • 163 103 905 220 159 ÷ 2 = 81 551 952 610 079 + 1;
  • 81 551 952 610 079 ÷ 2 = 40 775 976 305 039 + 1;
  • 40 775 976 305 039 ÷ 2 = 20 387 988 152 519 + 1;
  • 20 387 988 152 519 ÷ 2 = 10 193 994 076 259 + 1;
  • 10 193 994 076 259 ÷ 2 = 5 096 997 038 129 + 1;
  • 5 096 997 038 129 ÷ 2 = 2 548 498 519 064 + 1;
  • 2 548 498 519 064 ÷ 2 = 1 274 249 259 532 + 0;
  • 1 274 249 259 532 ÷ 2 = 637 124 629 766 + 0;
  • 637 124 629 766 ÷ 2 = 318 562 314 883 + 0;
  • 318 562 314 883 ÷ 2 = 159 281 157 441 + 1;
  • 159 281 157 441 ÷ 2 = 79 640 578 720 + 1;
  • 79 640 578 720 ÷ 2 = 39 820 289 360 + 0;
  • 39 820 289 360 ÷ 2 = 19 910 144 680 + 0;
  • 19 910 144 680 ÷ 2 = 9 955 072 340 + 0;
  • 9 955 072 340 ÷ 2 = 4 977 536 170 + 0;
  • 4 977 536 170 ÷ 2 = 2 488 768 085 + 0;
  • 2 488 768 085 ÷ 2 = 1 244 384 042 + 1;
  • 1 244 384 042 ÷ 2 = 622 192 021 + 0;
  • 622 192 021 ÷ 2 = 311 096 010 + 1;
  • 311 096 010 ÷ 2 = 155 548 005 + 0;
  • 155 548 005 ÷ 2 = 77 774 002 + 1;
  • 77 774 002 ÷ 2 = 38 887 001 + 0;
  • 38 887 001 ÷ 2 = 19 443 500 + 1;
  • 19 443 500 ÷ 2 = 9 721 750 + 0;
  • 9 721 750 ÷ 2 = 4 860 875 + 0;
  • 4 860 875 ÷ 2 = 2 430 437 + 1;
  • 2 430 437 ÷ 2 = 1 215 218 + 1;
  • 1 215 218 ÷ 2 = 607 609 + 0;
  • 607 609 ÷ 2 = 303 804 + 1;
  • 303 804 ÷ 2 = 151 902 + 0;
  • 151 902 ÷ 2 = 75 951 + 0;
  • 75 951 ÷ 2 = 37 975 + 1;
  • 37 975 ÷ 2 = 18 987 + 1;
  • 18 987 ÷ 2 = 9 493 + 1;
  • 9 493 ÷ 2 = 4 746 + 1;
  • 4 746 ÷ 2 = 2 373 + 0;
  • 2 373 ÷ 2 = 1 186 + 1;
  • 1 186 ÷ 2 = 593 + 0;
  • 593 ÷ 2 = 296 + 1;
  • 296 ÷ 2 = 148 + 0;
  • 148 ÷ 2 = 74 + 0;
  • 74 ÷ 2 = 37 + 0;
  • 37 ÷ 2 = 18 + 1;
  • 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.

1 336 147 191 563 544 666(10) = 1 0010 1000 1010 1111 0010 1100 1010 1010 0000 1100 0111 1110 1000 0101 1010(2)


4. Determine the signed binary number bit length:

  • The base 2 number's actual length, in bits: 61.

  • 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, 61,

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:


1 336 147 191 563 544 666(10) = 0001 0010 1000 1010 1111 0010 1100 1010 1010 0000 1100 0111 1110 1000 0101 1010

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...


-1 336 147 191 563 544 666(10) Base 10 integer number converted and written as a signed binary code (in base 2):

-1 336 147 191 563 544 666(10) = 1001 0010 1000 1010 1111 0010 1100 1010 1010 0000 1100 0111 1110 1000 0101 1010

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