Convert 1 001 000 010 000 783 to a Signed Binary (Base 2)

How to convert 1 001 000 010 000 783(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 1 001 000 010 000 783 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;
  • 1 001 000 010 000 783 ÷ 2 = 500 500 005 000 391 + 1;
  • 500 500 005 000 391 ÷ 2 = 250 250 002 500 195 + 1;
  • 250 250 002 500 195 ÷ 2 = 125 125 001 250 097 + 1;
  • 125 125 001 250 097 ÷ 2 = 62 562 500 625 048 + 1;
  • 62 562 500 625 048 ÷ 2 = 31 281 250 312 524 + 0;
  • 31 281 250 312 524 ÷ 2 = 15 640 625 156 262 + 0;
  • 15 640 625 156 262 ÷ 2 = 7 820 312 578 131 + 0;
  • 7 820 312 578 131 ÷ 2 = 3 910 156 289 065 + 1;
  • 3 910 156 289 065 ÷ 2 = 1 955 078 144 532 + 1;
  • 1 955 078 144 532 ÷ 2 = 977 539 072 266 + 0;
  • 977 539 072 266 ÷ 2 = 488 769 536 133 + 0;
  • 488 769 536 133 ÷ 2 = 244 384 768 066 + 1;
  • 244 384 768 066 ÷ 2 = 122 192 384 033 + 0;
  • 122 192 384 033 ÷ 2 = 61 096 192 016 + 1;
  • 61 096 192 016 ÷ 2 = 30 548 096 008 + 0;
  • 30 548 096 008 ÷ 2 = 15 274 048 004 + 0;
  • 15 274 048 004 ÷ 2 = 7 637 024 002 + 0;
  • 7 637 024 002 ÷ 2 = 3 818 512 001 + 0;
  • 3 818 512 001 ÷ 2 = 1 909 256 000 + 1;
  • 1 909 256 000 ÷ 2 = 954 628 000 + 0;
  • 954 628 000 ÷ 2 = 477 314 000 + 0;
  • 477 314 000 ÷ 2 = 238 657 000 + 0;
  • 238 657 000 ÷ 2 = 119 328 500 + 0;
  • 119 328 500 ÷ 2 = 59 664 250 + 0;
  • 59 664 250 ÷ 2 = 29 832 125 + 0;
  • 29 832 125 ÷ 2 = 14 916 062 + 1;
  • 14 916 062 ÷ 2 = 7 458 031 + 0;
  • 7 458 031 ÷ 2 = 3 729 015 + 1;
  • 3 729 015 ÷ 2 = 1 864 507 + 1;
  • 1 864 507 ÷ 2 = 932 253 + 1;
  • 932 253 ÷ 2 = 466 126 + 1;
  • 466 126 ÷ 2 = 233 063 + 0;
  • 233 063 ÷ 2 = 116 531 + 1;
  • 116 531 ÷ 2 = 58 265 + 1;
  • 58 265 ÷ 2 = 29 132 + 1;
  • 29 132 ÷ 2 = 14 566 + 0;
  • 14 566 ÷ 2 = 7 283 + 0;
  • 7 283 ÷ 2 = 3 641 + 1;
  • 3 641 ÷ 2 = 1 820 + 1;
  • 1 820 ÷ 2 = 910 + 0;
  • 910 ÷ 2 = 455 + 0;
  • 455 ÷ 2 = 227 + 1;
  • 227 ÷ 2 = 113 + 1;
  • 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;

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

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

1 001 000 010 000 783(10) = 11 1000 1110 0110 0111 0111 1010 0000 0100 0010 1001 1000 1111(2)


3. Determine the signed binary number bit length:

  • The base 2 number's actual length, in bits: 50.

  • 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, 50,

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:


1 001 000 010 000 783(10) Base 10 integer number converted and written as a signed binary code (in base 2):

1 001 000 010 000 783(10) = 0000 0000 0000 0011 1000 1110 0110 0111 0111 1010 0000 0100 0010 1001 1000 1111

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