Signed: Integer ↗ Binary: 100 001 001 110 106 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 100 001 001 110 106(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;
  • 100 001 001 110 106 ÷ 2 = 50 000 500 555 053 + 0;
  • 50 000 500 555 053 ÷ 2 = 25 000 250 277 526 + 1;
  • 25 000 250 277 526 ÷ 2 = 12 500 125 138 763 + 0;
  • 12 500 125 138 763 ÷ 2 = 6 250 062 569 381 + 1;
  • 6 250 062 569 381 ÷ 2 = 3 125 031 284 690 + 1;
  • 3 125 031 284 690 ÷ 2 = 1 562 515 642 345 + 0;
  • 1 562 515 642 345 ÷ 2 = 781 257 821 172 + 1;
  • 781 257 821 172 ÷ 2 = 390 628 910 586 + 0;
  • 390 628 910 586 ÷ 2 = 195 314 455 293 + 0;
  • 195 314 455 293 ÷ 2 = 97 657 227 646 + 1;
  • 97 657 227 646 ÷ 2 = 48 828 613 823 + 0;
  • 48 828 613 823 ÷ 2 = 24 414 306 911 + 1;
  • 24 414 306 911 ÷ 2 = 12 207 153 455 + 1;
  • 12 207 153 455 ÷ 2 = 6 103 576 727 + 1;
  • 6 103 576 727 ÷ 2 = 3 051 788 363 + 1;
  • 3 051 788 363 ÷ 2 = 1 525 894 181 + 1;
  • 1 525 894 181 ÷ 2 = 762 947 090 + 1;
  • 762 947 090 ÷ 2 = 381 473 545 + 0;
  • 381 473 545 ÷ 2 = 190 736 772 + 1;
  • 190 736 772 ÷ 2 = 95 368 386 + 0;
  • 95 368 386 ÷ 2 = 47 684 193 + 0;
  • 47 684 193 ÷ 2 = 23 842 096 + 1;
  • 23 842 096 ÷ 2 = 11 921 048 + 0;
  • 11 921 048 ÷ 2 = 5 960 524 + 0;
  • 5 960 524 ÷ 2 = 2 980 262 + 0;
  • 2 980 262 ÷ 2 = 1 490 131 + 0;
  • 1 490 131 ÷ 2 = 745 065 + 1;
  • 745 065 ÷ 2 = 372 532 + 1;
  • 372 532 ÷ 2 = 186 266 + 0;
  • 186 266 ÷ 2 = 93 133 + 0;
  • 93 133 ÷ 2 = 46 566 + 1;
  • 46 566 ÷ 2 = 23 283 + 0;
  • 23 283 ÷ 2 = 11 641 + 1;
  • 11 641 ÷ 2 = 5 820 + 1;
  • 5 820 ÷ 2 = 2 910 + 0;
  • 2 910 ÷ 2 = 1 455 + 0;
  • 1 455 ÷ 2 = 727 + 1;
  • 727 ÷ 2 = 363 + 1;
  • 363 ÷ 2 = 181 + 1;
  • 181 ÷ 2 = 90 + 1;
  • 90 ÷ 2 = 45 + 0;
  • 45 ÷ 2 = 22 + 1;
  • 22 ÷ 2 = 11 + 0;
  • 11 ÷ 2 = 5 + 1;
  • 5 ÷ 2 = 2 + 1;
  • 2 ÷ 2 = 1 + 0;
  • 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.


100 001 001 110 106(10) = 101 1010 1111 0011 0100 1100 0010 0101 1111 1010 0101 1010(2)


3. 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.


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 100 001 001 110 106(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):

100 001 001 110 106(10) = 0000 0000 0000 0000 0101 1010 1111 0011 0100 1100 0010 0101 1111 1010 0101 1010

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

More operations on signed integer numbers:

» Signed integer number 100 001 001 110 105 converted from decimal system (from base 10) and written as a signed binary (in base 2) = ?

» Signed integer number 100 001 001 110 107 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