Signed: Integer ↗ Binary: 10 001 010 001 110 011 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 10 001 010 001 110 011(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;
  • 10 001 010 001 110 011 ÷ 2 = 5 000 505 000 555 005 + 1;
  • 5 000 505 000 555 005 ÷ 2 = 2 500 252 500 277 502 + 1;
  • 2 500 252 500 277 502 ÷ 2 = 1 250 126 250 138 751 + 0;
  • 1 250 126 250 138 751 ÷ 2 = 625 063 125 069 375 + 1;
  • 625 063 125 069 375 ÷ 2 = 312 531 562 534 687 + 1;
  • 312 531 562 534 687 ÷ 2 = 156 265 781 267 343 + 1;
  • 156 265 781 267 343 ÷ 2 = 78 132 890 633 671 + 1;
  • 78 132 890 633 671 ÷ 2 = 39 066 445 316 835 + 1;
  • 39 066 445 316 835 ÷ 2 = 19 533 222 658 417 + 1;
  • 19 533 222 658 417 ÷ 2 = 9 766 611 329 208 + 1;
  • 9 766 611 329 208 ÷ 2 = 4 883 305 664 604 + 0;
  • 4 883 305 664 604 ÷ 2 = 2 441 652 832 302 + 0;
  • 2 441 652 832 302 ÷ 2 = 1 220 826 416 151 + 0;
  • 1 220 826 416 151 ÷ 2 = 610 413 208 075 + 1;
  • 610 413 208 075 ÷ 2 = 305 206 604 037 + 1;
  • 305 206 604 037 ÷ 2 = 152 603 302 018 + 1;
  • 152 603 302 018 ÷ 2 = 76 301 651 009 + 0;
  • 76 301 651 009 ÷ 2 = 38 150 825 504 + 1;
  • 38 150 825 504 ÷ 2 = 19 075 412 752 + 0;
  • 19 075 412 752 ÷ 2 = 9 537 706 376 + 0;
  • 9 537 706 376 ÷ 2 = 4 768 853 188 + 0;
  • 4 768 853 188 ÷ 2 = 2 384 426 594 + 0;
  • 2 384 426 594 ÷ 2 = 1 192 213 297 + 0;
  • 1 192 213 297 ÷ 2 = 596 106 648 + 1;
  • 596 106 648 ÷ 2 = 298 053 324 + 0;
  • 298 053 324 ÷ 2 = 149 026 662 + 0;
  • 149 026 662 ÷ 2 = 74 513 331 + 0;
  • 74 513 331 ÷ 2 = 37 256 665 + 1;
  • 37 256 665 ÷ 2 = 18 628 332 + 1;
  • 18 628 332 ÷ 2 = 9 314 166 + 0;
  • 9 314 166 ÷ 2 = 4 657 083 + 0;
  • 4 657 083 ÷ 2 = 2 328 541 + 1;
  • 2 328 541 ÷ 2 = 1 164 270 + 1;
  • 1 164 270 ÷ 2 = 582 135 + 0;
  • 582 135 ÷ 2 = 291 067 + 1;
  • 291 067 ÷ 2 = 145 533 + 1;
  • 145 533 ÷ 2 = 72 766 + 1;
  • 72 766 ÷ 2 = 36 383 + 0;
  • 36 383 ÷ 2 = 18 191 + 1;
  • 18 191 ÷ 2 = 9 095 + 1;
  • 9 095 ÷ 2 = 4 547 + 1;
  • 4 547 ÷ 2 = 2 273 + 1;
  • 2 273 ÷ 2 = 1 136 + 1;
  • 1 136 ÷ 2 = 568 + 0;
  • 568 ÷ 2 = 284 + 0;
  • 284 ÷ 2 = 142 + 0;
  • 142 ÷ 2 = 71 + 0;
  • 71 ÷ 2 = 35 + 1;
  • 35 ÷ 2 = 17 + 1;
  • 17 ÷ 2 = 8 + 1;
  • 8 ÷ 2 = 4 + 0;
  • 4 ÷ 2 = 2 + 0;
  • 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.


10 001 010 001 110 011(10) = 10 0011 1000 0111 1101 1101 1001 1000 1000 0010 1110 0011 1111 1011(2)


3. Determine the signed binary number bit length:

The base 2 number's actual length, in bits: 54.

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, 54,

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 10 001 010 001 110 011(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):

10 001 010 001 110 011(10) = 0000 0000 0010 0011 1000 0111 1101 1101 1001 1000 1000 0010 1110 0011 1111 1011

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

More operations on signed integer numbers:

» Signed integer number 10 001 010 001 110 010 converted from decimal system (from base 10) and written as a signed binary (in base 2) = ?

» Signed integer number 10 001 010 001 110 012 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