Convert 101 010 101 112 to signed binary, from a base 10 decimal system signed integer number

101 010 101 112(10) to a signed binary = ?

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;
  • 101 010 101 112 ÷ 2 = 50 505 050 556 + 0;
  • 50 505 050 556 ÷ 2 = 25 252 525 278 + 0;
  • 25 252 525 278 ÷ 2 = 12 626 262 639 + 0;
  • 12 626 262 639 ÷ 2 = 6 313 131 319 + 1;
  • 6 313 131 319 ÷ 2 = 3 156 565 659 + 1;
  • 3 156 565 659 ÷ 2 = 1 578 282 829 + 1;
  • 1 578 282 829 ÷ 2 = 789 141 414 + 1;
  • 789 141 414 ÷ 2 = 394 570 707 + 0;
  • 394 570 707 ÷ 2 = 197 285 353 + 1;
  • 197 285 353 ÷ 2 = 98 642 676 + 1;
  • 98 642 676 ÷ 2 = 49 321 338 + 0;
  • 49 321 338 ÷ 2 = 24 660 669 + 0;
  • 24 660 669 ÷ 2 = 12 330 334 + 1;
  • 12 330 334 ÷ 2 = 6 165 167 + 0;
  • 6 165 167 ÷ 2 = 3 082 583 + 1;
  • 3 082 583 ÷ 2 = 1 541 291 + 1;
  • 1 541 291 ÷ 2 = 770 645 + 1;
  • 770 645 ÷ 2 = 385 322 + 1;
  • 385 322 ÷ 2 = 192 661 + 0;
  • 192 661 ÷ 2 = 96 330 + 1;
  • 96 330 ÷ 2 = 48 165 + 0;
  • 48 165 ÷ 2 = 24 082 + 1;
  • 24 082 ÷ 2 = 12 041 + 0;
  • 12 041 ÷ 2 = 6 020 + 1;
  • 6 020 ÷ 2 = 3 010 + 0;
  • 3 010 ÷ 2 = 1 505 + 0;
  • 1 505 ÷ 2 = 752 + 1;
  • 752 ÷ 2 = 376 + 0;
  • 376 ÷ 2 = 188 + 0;
  • 188 ÷ 2 = 94 + 0;
  • 94 ÷ 2 = 47 + 0;
  • 47 ÷ 2 = 23 + 1;
  • 23 ÷ 2 = 11 + 1;
  • 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.

101 010 101 112(10) = 1 0111 1000 0100 1010 1011 1101 0011 0111 1000(2)


3. Determine the signed binary number bit length:

The base 2 number's actual length, in bits: 37.

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; ...

First bit (the leftmost) is reserved for the sign:
0 = positive integer number, 1 = negative integer number

The least number that is:


a power of 2


and is larger than the actual length, 37,


so that the first bit (leftmost) could be zero


(we deal with a positive number at this moment)


is: 64.


4. 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:

101 010 101 112(10) = 0000 0000 0000 0000 0000 0000 0001 0111 1000 0100 1010 1011 1101 0011 0111 1000


Number 101 010 101 112, a signed integer, converted from decimal system (base 10) to signed binary:

101 010 101 112(10) = 0000 0000 0000 0000 0000 0000 0001 0111 1000 0100 1010 1011 1101 0011 0111 1000

First bit (the leftmost) is reserved for the sign:
0 = positive integer number, 1 = negative integer number

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


More operations of this kind:

101 010 101 111 = ? | Signed integer 101 010 101 113 = ?


Convert signed integer numbers from the decimal system (base ten) to signed binary

How to convert a base 10 signed integer number to signed binary:

1) Divide the positive version of number repeatedly by 2, keeping track of each remainder, till getting a quotient that is 0.

2) Construct the base 2 representation by taking the previously calculated remainders starting from the last remainder up to the first one, in that order.

3) Construct the positive binary computer representation so that the first bit is 0.

4) Only if the initial number is negative, change the first bit (the leftmost), from 0 to 1. The leftmost bit is reserved for the sign, 1 = negative, 0 = positive.

Latest signed integer numbers in decimal (base ten) converted to signed binary

101,010,101,112 to signed binary = ? May 12 07:03 UTC (GMT)
99,999,973 to signed binary = ? May 12 07:03 UTC (GMT)
-65,256 to signed binary = ? May 12 07:03 UTC (GMT)
1,111,101,090 to signed binary = ? May 12 07:03 UTC (GMT)
33,554,407 to signed binary = ? May 12 07:03 UTC (GMT)
-262,278 to signed binary = ? May 12 07:03 UTC (GMT)
-50,577 to signed binary = ? May 12 07:03 UTC (GMT)
-27,182,828,294 to signed binary = ? May 12 07:03 UTC (GMT)
1,101,133 to signed binary = ? May 12 07:03 UTC (GMT)
100,100,100,109 to signed binary = ? May 12 07:03 UTC (GMT)
5,964 to signed binary = ? May 12 07:02 UTC (GMT)
-503,316,488 to signed binary = ? May 12 07:02 UTC (GMT)
262,144 to signed binary = ? May 12 07:02 UTC (GMT)
All decimal positive integers converted to signed binary

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