Signed: Integer ↗ Binary: 101 000 010 101 187 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 101 000 010 101 187(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;
  • 101 000 010 101 187 ÷ 2 = 50 500 005 050 593 + 1;
  • 50 500 005 050 593 ÷ 2 = 25 250 002 525 296 + 1;
  • 25 250 002 525 296 ÷ 2 = 12 625 001 262 648 + 0;
  • 12 625 001 262 648 ÷ 2 = 6 312 500 631 324 + 0;
  • 6 312 500 631 324 ÷ 2 = 3 156 250 315 662 + 0;
  • 3 156 250 315 662 ÷ 2 = 1 578 125 157 831 + 0;
  • 1 578 125 157 831 ÷ 2 = 789 062 578 915 + 1;
  • 789 062 578 915 ÷ 2 = 394 531 289 457 + 1;
  • 394 531 289 457 ÷ 2 = 197 265 644 728 + 1;
  • 197 265 644 728 ÷ 2 = 98 632 822 364 + 0;
  • 98 632 822 364 ÷ 2 = 49 316 411 182 + 0;
  • 49 316 411 182 ÷ 2 = 24 658 205 591 + 0;
  • 24 658 205 591 ÷ 2 = 12 329 102 795 + 1;
  • 12 329 102 795 ÷ 2 = 6 164 551 397 + 1;
  • 6 164 551 397 ÷ 2 = 3 082 275 698 + 1;
  • 3 082 275 698 ÷ 2 = 1 541 137 849 + 0;
  • 1 541 137 849 ÷ 2 = 770 568 924 + 1;
  • 770 568 924 ÷ 2 = 385 284 462 + 0;
  • 385 284 462 ÷ 2 = 192 642 231 + 0;
  • 192 642 231 ÷ 2 = 96 321 115 + 1;
  • 96 321 115 ÷ 2 = 48 160 557 + 1;
  • 48 160 557 ÷ 2 = 24 080 278 + 1;
  • 24 080 278 ÷ 2 = 12 040 139 + 0;
  • 12 040 139 ÷ 2 = 6 020 069 + 1;
  • 6 020 069 ÷ 2 = 3 010 034 + 1;
  • 3 010 034 ÷ 2 = 1 505 017 + 0;
  • 1 505 017 ÷ 2 = 752 508 + 1;
  • 752 508 ÷ 2 = 376 254 + 0;
  • 376 254 ÷ 2 = 188 127 + 0;
  • 188 127 ÷ 2 = 94 063 + 1;
  • 94 063 ÷ 2 = 47 031 + 1;
  • 47 031 ÷ 2 = 23 515 + 1;
  • 23 515 ÷ 2 = 11 757 + 1;
  • 11 757 ÷ 2 = 5 878 + 1;
  • 5 878 ÷ 2 = 2 939 + 0;
  • 2 939 ÷ 2 = 1 469 + 1;
  • 1 469 ÷ 2 = 734 + 1;
  • 734 ÷ 2 = 367 + 0;
  • 367 ÷ 2 = 183 + 1;
  • 183 ÷ 2 = 91 + 1;
  • 91 ÷ 2 = 45 + 1;
  • 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.


101 000 010 101 187(10) = 101 1011 1101 1011 1110 0101 1011 1001 0111 0001 1100 0011(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 101 000 010 101 187(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):

101 000 010 101 187(10) = 0000 0000 0000 0000 0101 1011 1101 1011 1110 0101 1011 1001 0111 0001 1100 0011

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

More operations on signed integer numbers:

» Signed integer number 101 000 010 101 186 converted from decimal system (from base 10) and written as a signed binary (in base 2) = ?

» Signed integer number 101 000 010 101 188 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