Signed: Integer ↗ Binary: 1 000 000 010 000 023 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 1 000 000 010 000 023(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;
  • 1 000 000 010 000 023 ÷ 2 = 500 000 005 000 011 + 1;
  • 500 000 005 000 011 ÷ 2 = 250 000 002 500 005 + 1;
  • 250 000 002 500 005 ÷ 2 = 125 000 001 250 002 + 1;
  • 125 000 001 250 002 ÷ 2 = 62 500 000 625 001 + 0;
  • 62 500 000 625 001 ÷ 2 = 31 250 000 312 500 + 1;
  • 31 250 000 312 500 ÷ 2 = 15 625 000 156 250 + 0;
  • 15 625 000 156 250 ÷ 2 = 7 812 500 078 125 + 0;
  • 7 812 500 078 125 ÷ 2 = 3 906 250 039 062 + 1;
  • 3 906 250 039 062 ÷ 2 = 1 953 125 019 531 + 0;
  • 1 953 125 019 531 ÷ 2 = 976 562 509 765 + 1;
  • 976 562 509 765 ÷ 2 = 488 281 254 882 + 1;
  • 488 281 254 882 ÷ 2 = 244 140 627 441 + 0;
  • 244 140 627 441 ÷ 2 = 122 070 313 720 + 1;
  • 122 070 313 720 ÷ 2 = 61 035 156 860 + 0;
  • 61 035 156 860 ÷ 2 = 30 517 578 430 + 0;
  • 30 517 578 430 ÷ 2 = 15 258 789 215 + 0;
  • 15 258 789 215 ÷ 2 = 7 629 394 607 + 1;
  • 7 629 394 607 ÷ 2 = 3 814 697 303 + 1;
  • 3 814 697 303 ÷ 2 = 1 907 348 651 + 1;
  • 1 907 348 651 ÷ 2 = 953 674 325 + 1;
  • 953 674 325 ÷ 2 = 476 837 162 + 1;
  • 476 837 162 ÷ 2 = 238 418 581 + 0;
  • 238 418 581 ÷ 2 = 119 209 290 + 1;
  • 119 209 290 ÷ 2 = 59 604 645 + 0;
  • 59 604 645 ÷ 2 = 29 802 322 + 1;
  • 29 802 322 ÷ 2 = 14 901 161 + 0;
  • 14 901 161 ÷ 2 = 7 450 580 + 1;
  • 7 450 580 ÷ 2 = 3 725 290 + 0;
  • 3 725 290 ÷ 2 = 1 862 645 + 0;
  • 1 862 645 ÷ 2 = 931 322 + 1;
  • 931 322 ÷ 2 = 465 661 + 0;
  • 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.


1 000 000 010 000 023(10) = 11 1000 1101 0111 1110 1010 0101 0101 1111 0001 0110 1001 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 1 000 000 010 000 023(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):

1 000 000 010 000 023(10) = 0000 0000 0000 0011 1000 1101 0111 1110 1010 0101 0101 1111 0001 0110 1001 0111

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

More operations on signed integer numbers:

» Signed integer number 1 000 000 010 000 022 converted from decimal system (from base 10) and written as a signed binary (in base 2) = ?

» Signed integer number 1 000 000 010 000 024 converted from decimal system (from base 10) and written as a signed binary (in base 2) = ?

The latest signed integer numbers (that are written in decimal system, in base ten) converted and written as signed binary numbers

Convert the base ten decimal system integer number 19,999,999,999,994, write it as a signed binary written in base two Apr 20 07:58 UTC (GMT)
Convert the base ten decimal system integer number -2,684,503,429, write it as a signed binary written in base two Apr 20 07:58 UTC (GMT)
Convert the base ten decimal system integer number 100,111,000,008, write it as a signed binary written in base two Apr 20 07:58 UTC (GMT)
Convert the base ten decimal system integer number 60,922, write it as a signed binary written in base two Apr 20 07:57 UTC (GMT)
Convert the base ten decimal system integer number 1,001,001,005, write it as a signed binary written in base two Apr 20 07:57 UTC (GMT)
Convert the base ten decimal system integer number 10,100,000,238, write it as a signed binary written in base two Apr 20 07:57 UTC (GMT)
Convert the base ten decimal system integer number 67,804, write it as a signed binary written in base two Apr 20 07:57 UTC (GMT)
Convert the base ten decimal system integer number 192,803, write it as a signed binary written in base two Apr 20 07:57 UTC (GMT)
Convert the base ten decimal system integer number 1,141, write it as a signed binary written in base two Apr 20 07:57 UTC (GMT)
Convert the base ten decimal system integer number -6,467, write it as a signed binary written in base two Apr 20 07:57 UTC (GMT)
All the decimal system integer numbers (written in base ten) converted and written as signed binary numbers

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