Convert 10 101 111 010 to a signed binary in one's complement representation, from a base 10 decimal system signed integer number

10 101 111 010(10) to a signed binary one's complement representation = ?

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;
  • 10 101 111 010 ÷ 2 = 5 050 555 505 + 0;
  • 5 050 555 505 ÷ 2 = 2 525 277 752 + 1;
  • 2 525 277 752 ÷ 2 = 1 262 638 876 + 0;
  • 1 262 638 876 ÷ 2 = 631 319 438 + 0;
  • 631 319 438 ÷ 2 = 315 659 719 + 0;
  • 315 659 719 ÷ 2 = 157 829 859 + 1;
  • 157 829 859 ÷ 2 = 78 914 929 + 1;
  • 78 914 929 ÷ 2 = 39 457 464 + 1;
  • 39 457 464 ÷ 2 = 19 728 732 + 0;
  • 19 728 732 ÷ 2 = 9 864 366 + 0;
  • 9 864 366 ÷ 2 = 4 932 183 + 0;
  • 4 932 183 ÷ 2 = 2 466 091 + 1;
  • 2 466 091 ÷ 2 = 1 233 045 + 1;
  • 1 233 045 ÷ 2 = 616 522 + 1;
  • 616 522 ÷ 2 = 308 261 + 0;
  • 308 261 ÷ 2 = 154 130 + 1;
  • 154 130 ÷ 2 = 77 065 + 0;
  • 77 065 ÷ 2 = 38 532 + 1;
  • 38 532 ÷ 2 = 19 266 + 0;
  • 19 266 ÷ 2 = 9 633 + 0;
  • 9 633 ÷ 2 = 4 816 + 1;
  • 4 816 ÷ 2 = 2 408 + 0;
  • 2 408 ÷ 2 = 1 204 + 0;
  • 1 204 ÷ 2 = 602 + 0;
  • 602 ÷ 2 = 301 + 0;
  • 301 ÷ 2 = 150 + 1;
  • 150 ÷ 2 = 75 + 0;
  • 75 ÷ 2 = 37 + 1;
  • 37 ÷ 2 = 18 + 1;
  • 18 ÷ 2 = 9 + 0;
  • 9 ÷ 2 = 4 + 1;
  • 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.

10 101 111 010(10) = 10 0101 1010 0001 0010 1011 1000 1110 0010(2)


3. Determine the signed binary number bit length:

The base 2 number's actual length, in bits: 34.

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) indicates the sign,
1 = negative, 0 = positive.

The least number that is:


a power of 2


and is larger than the actual length, 34,


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:

10 101 111 010(10) = 0000 0000 0000 0000 0000 0000 0000 0010 0101 1010 0001 0010 1011 1000 1110 0010


Number 10 101 111 010, a signed integer, converted from decimal system (base 10) to a signed binary one's complement representation:

10 101 111 010(10) = 0000 0000 0000 0000 0000 0000 0000 0010 0101 1010 0001 0010 1011 1000 1110 0010

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


More operations of this kind:

10 101 111 009 = ? | 10 101 111 011 = ?


Convert signed integer numbers from the decimal system (base ten) to signed binary one's complement representation

How to convert a base 10 signed integer number to signed binary in one's complement representation:

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, switch all the bits from 0 to 1 and from 1 to 0 (reversing the digits).

Latest signed integer numbers converted from decimal system to signed binary in one's complement representation

10,101,111,010 to signed binary one's complement = ? Jul 24 09:52 UTC (GMT)
1,111,110,101,100,113 to signed binary one's complement = ? Jul 24 09:51 UTC (GMT)
78 to signed binary one's complement = ? Jul 24 09:51 UTC (GMT)
26,874 to signed binary one's complement = ? Jul 24 09:51 UTC (GMT)
110,001,124 to signed binary one's complement = ? Jul 24 09:51 UTC (GMT)
22,330 to signed binary one's complement = ? Jul 24 09:50 UTC (GMT)
-33,554,416 to signed binary one's complement = ? Jul 24 09:49 UTC (GMT)
-88 to signed binary one's complement = ? Jul 24 09:48 UTC (GMT)
1,000,287 to signed binary one's complement = ? Jul 24 09:48 UTC (GMT)
6,696 to signed binary one's complement = ? Jul 24 09:48 UTC (GMT)
10,000,104 to signed binary one's complement = ? Jul 24 09:48 UTC (GMT)
43,122 to signed binary one's complement = ? Jul 24 09:48 UTC (GMT)
-19 to signed binary one's complement = ? Jul 24 09:47 UTC (GMT)
All decimal integer numbers converted to signed binary one's complement representation

How to convert signed integers from the decimal system to signed binary in one's complement representation

Follow the steps below to convert a signed base 10 integer number to signed binary in one's complement representation:

  • 1. If the number to be converted is negative, start with the positive version of the number.
  • 2. Divide repeatedly by 2 the positive representation of the integer number that is to be converted to binary, keeping track of each remainder, until we get a quotient that is equal to 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 must have 4, 8, 16, 32, 64, ... bit length (a power of 2) - if needed, fill in '0' bits in front (to the left) of the base 2 number calculated above, up to the right length; this way the first bit (leftmost) will always be '0', correctly representing a positive number.
  • 5. To get the negative integer number representation in signed binary one's complement, replace all '0' bits with '1's and all '1' bits with '0's.

Example: convert the negative number -49 from the decimal system (base ten) to signed binary one's complement:

  • 1. Start with the positive version of the number: |-49| = 49
  • 2. Divide repeatedly 49 by 2, keeping track of each remainder:
    • division = quotient + remainder
    • 49 ÷ 2 = 24 + 1
    • 24 ÷ 2 = 12 + 0
    • 12 ÷ 2 = 6 + 0
    • 6 ÷ 2 = 3 + 0
    • 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:
    49(10) = 11 0001(2)
  • 4. The actual bit length of base 2 representation is 6, so the positive binary computer representation of a signed binary will take in this case 8 bits (the least power of 2 that is larger than 6) - add '0's in front of the base 2 number, up to the required length:
    49(10) = 0011 0001(2)
  • 5. To get the negative integer number representation in signed binary one's complement, replace all '0' bits with '1's and all '1' bits with '0's:
    -49(10) = 1100 1110
  • Number -49(10), signed integer, converted from the decimal system (base 10) to signed binary in one's complement representation = 1100 1110