Signed: Integer ↗ Binary: 1 000 001 111 100 007 Convert the Integer Number to a Signed Binary. Converting and Writing the Base Ten Decimal System Signed Integer as Binary Code (Written in Base Two)

Signed integer number 1 000 001 111 100 007(10)
converted and written as a signed binary (base 2) = ?

1. Divide the number repeatedly by 2:

Keep track of each remainder.

We stop when we get a quotient that is equal to zero.


  • division = quotient + remainder;
  • 1 000 001 111 100 007 ÷ 2 = 500 000 555 550 003 + 1;
  • 500 000 555 550 003 ÷ 2 = 250 000 277 775 001 + 1;
  • 250 000 277 775 001 ÷ 2 = 125 000 138 887 500 + 1;
  • 125 000 138 887 500 ÷ 2 = 62 500 069 443 750 + 0;
  • 62 500 069 443 750 ÷ 2 = 31 250 034 721 875 + 0;
  • 31 250 034 721 875 ÷ 2 = 15 625 017 360 937 + 1;
  • 15 625 017 360 937 ÷ 2 = 7 812 508 680 468 + 1;
  • 7 812 508 680 468 ÷ 2 = 3 906 254 340 234 + 0;
  • 3 906 254 340 234 ÷ 2 = 1 953 127 170 117 + 0;
  • 1 953 127 170 117 ÷ 2 = 976 563 585 058 + 1;
  • 976 563 585 058 ÷ 2 = 488 281 792 529 + 0;
  • 488 281 792 529 ÷ 2 = 244 140 896 264 + 1;
  • 244 140 896 264 ÷ 2 = 122 070 448 132 + 0;
  • 122 070 448 132 ÷ 2 = 61 035 224 066 + 0;
  • 61 035 224 066 ÷ 2 = 30 517 612 033 + 0;
  • 30 517 612 033 ÷ 2 = 15 258 806 016 + 1;
  • 15 258 806 016 ÷ 2 = 7 629 403 008 + 0;
  • 7 629 403 008 ÷ 2 = 3 814 701 504 + 0;
  • 3 814 701 504 ÷ 2 = 1 907 350 752 + 0;
  • 1 907 350 752 ÷ 2 = 953 675 376 + 0;
  • 953 675 376 ÷ 2 = 476 837 688 + 0;
  • 476 837 688 ÷ 2 = 238 418 844 + 0;
  • 238 418 844 ÷ 2 = 119 209 422 + 0;
  • 119 209 422 ÷ 2 = 59 604 711 + 0;
  • 59 604 711 ÷ 2 = 29 802 355 + 1;
  • 29 802 355 ÷ 2 = 14 901 177 + 1;
  • 14 901 177 ÷ 2 = 7 450 588 + 1;
  • 7 450 588 ÷ 2 = 3 725 294 + 0;
  • 3 725 294 ÷ 2 = 1 862 647 + 0;
  • 1 862 647 ÷ 2 = 931 323 + 1;
  • 931 323 ÷ 2 = 465 661 + 1;
  • 465 661 ÷ 2 = 232 830 + 1;
  • 232 830 ÷ 2 = 116 415 + 0;
  • 116 415 ÷ 2 = 58 207 + 1;
  • 58 207 ÷ 2 = 29 103 + 1;
  • 29 103 ÷ 2 = 14 551 + 1;
  • 14 551 ÷ 2 = 7 275 + 1;
  • 7 275 ÷ 2 = 3 637 + 1;
  • 3 637 ÷ 2 = 1 818 + 1;
  • 1 818 ÷ 2 = 909 + 0;
  • 909 ÷ 2 = 454 + 1;
  • 454 ÷ 2 = 227 + 0;
  • 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.


1 000 001 111 100 007(10) = 11 1000 1101 0111 1110 1110 0111 0000 0000 1000 1010 0110 0111(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:


Number 1 000 001 111 100 007(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):

1 000 001 111 100 007(10) = 0000 0000 0000 0011 1000 1101 0111 1110 1110 0111 0000 0000 1000 1010 0110 0111

Spaces were used to group digits: for binary, by 4, for decimal, by 3.

More operations on signed integer numbers:

» Signed integer number 1 000 001 111 100 006 converted from decimal system (from base 10) and written as a signed binary (in base 2) = ?

» Signed integer number 1 000 001 111 100 008 converted from decimal system (from base 10) and written as a signed binary (in base 2) = ?

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How to convert signed integers from decimal system 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