Convert 10 000 111 to a signed binary in one's complement representation, from a base 10 decimal system signed integer number

10 000 111(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;
  • 10 000 111 ÷ 2 = 5 000 055 + 1;
  • 5 000 055 ÷ 2 = 2 500 027 + 1;
  • 2 500 027 ÷ 2 = 1 250 013 + 1;
  • 1 250 013 ÷ 2 = 625 006 + 1;
  • 625 006 ÷ 2 = 312 503 + 0;
  • 312 503 ÷ 2 = 156 251 + 1;
  • 156 251 ÷ 2 = 78 125 + 1;
  • 78 125 ÷ 2 = 39 062 + 1;
  • 39 062 ÷ 2 = 19 531 + 0;
  • 19 531 ÷ 2 = 9 765 + 1;
  • 9 765 ÷ 2 = 4 882 + 1;
  • 4 882 ÷ 2 = 2 441 + 0;
  • 2 441 ÷ 2 = 1 220 + 1;
  • 1 220 ÷ 2 = 610 + 0;
  • 610 ÷ 2 = 305 + 0;
  • 305 ÷ 2 = 152 + 1;
  • 152 ÷ 2 = 76 + 0;
  • 76 ÷ 2 = 38 + 0;
  • 38 ÷ 2 = 19 + 0;
  • 19 ÷ 2 = 9 + 1;
  • 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.

10 000 111(10) = 1001 1000 1001 0110 1110 1111(2)


3. Determine the signed binary number bit length:

The base 2 number's actual length, in bits: 24.

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, 24,


so that the first bit (leftmost) could be zero


(we deal with a positive number at this moment)


is: 32.


4. Positive binary computer representation on 32 bits (4 Bytes):

If needed, add extra 0s in front (to the left) of the base 2 number, up to the required length, 32:

10 000 111(10) = 0000 0000 1001 1000 1001 0110 1110 1111


Number 10 000 111, a signed integer, converted from decimal system (base 10) to a signed binary one's complement representation:

10 000 111(10) = 0000 0000 1001 1000 1001 0110 1110 1111

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


More operations of this kind:

10 000 110 = ? | 10 000 112 = ?


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

10,000,111 to signed binary one's complement = ? May 12 07:48 UTC (GMT)
35 to signed binary one's complement = ? May 12 07:47 UTC (GMT)
2,015,042,700 to signed binary one's complement = ? May 12 07:47 UTC (GMT)
62,317 to signed binary one's complement = ? May 12 07:47 UTC (GMT)
1,000,979 to signed binary one's complement = ? May 12 07:45 UTC (GMT)
22,169 to signed binary one's complement = ? May 12 07:45 UTC (GMT)
19,127,337 to signed binary one's complement = ? May 12 07:45 UTC (GMT)
-60,508 to signed binary one's complement = ? May 12 07:44 UTC (GMT)
9,999,999,993 to signed binary one's complement = ? May 12 07:44 UTC (GMT)
10,111,010,110 to signed binary one's complement = ? May 12 07:44 UTC (GMT)
11,121,596 to signed binary one's complement = ? May 12 07:43 UTC (GMT)
58,253 to signed binary one's complement = ? May 12 07:43 UTC (GMT)
1,100,101,007 to signed binary one's complement = ? May 12 07:43 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