Convert -9 533 052 to a signed binary in one's complement representation, from a base 10 decimal system signed integer number

-9 533 052(10) to a signed binary one's complement representation = ?

1. Start with the positive version of the number:

|-9 533 052| = 9 533 052

2. 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;
  • 9 533 052 ÷ 2 = 4 766 526 + 0;
  • 4 766 526 ÷ 2 = 2 383 263 + 0;
  • 2 383 263 ÷ 2 = 1 191 631 + 1;
  • 1 191 631 ÷ 2 = 595 815 + 1;
  • 595 815 ÷ 2 = 297 907 + 1;
  • 297 907 ÷ 2 = 148 953 + 1;
  • 148 953 ÷ 2 = 74 476 + 1;
  • 74 476 ÷ 2 = 37 238 + 0;
  • 37 238 ÷ 2 = 18 619 + 0;
  • 18 619 ÷ 2 = 9 309 + 1;
  • 9 309 ÷ 2 = 4 654 + 1;
  • 4 654 ÷ 2 = 2 327 + 0;
  • 2 327 ÷ 2 = 1 163 + 1;
  • 1 163 ÷ 2 = 581 + 1;
  • 581 ÷ 2 = 290 + 1;
  • 290 ÷ 2 = 145 + 0;
  • 145 ÷ 2 = 72 + 1;
  • 72 ÷ 2 = 36 + 0;
  • 36 ÷ 2 = 18 + 0;
  • 18 ÷ 2 = 9 + 0;
  • 9 ÷ 2 = 4 + 1;
  • 4 ÷ 2 = 2 + 0;
  • 2 ÷ 2 = 1 + 0;
  • 1 ÷ 2 = 0 + 1;

3. Construct the base 2 representation of the positive number:

Take all the remainders starting from the bottom of the list constructed above.

9 533 052(10) = 1001 0001 0111 0110 0111 1100(2)


4. 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.


5. 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:

9 533 052(10) = 0000 0000 1001 0001 0111 0110 0111 1100


6. Get the negative integer number representation:

To get the negative integer number representation on 32 bits (4 Bytes),


signed binary one's complement,


replace all the bits on 0 with 1s


and all the bits set on 1 with 0s


(reverse the digits, flip the digits)


!(0000 0000 1001 0001 0111 0110 0111 1100) =


1111 1111 0110 1110 1000 1001 1000 0011


Number -9 533 052, a signed integer, converted from decimal system (base 10) to a signed binary one's complement representation:

-9 533 052(10) = 1111 1111 0110 1110 1000 1001 1000 0011

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


More operations of this kind:

-9 533 053 = ? | -9 533 051 = ?


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

-9,533,052 to signed binary one's complement = ? Sep 20 03:20 UTC (GMT)
-126 to signed binary one's complement = ? Sep 20 03:20 UTC (GMT)
-16,397 to signed binary one's complement = ? Sep 20 03:19 UTC (GMT)
-54 to signed binary one's complement = ? Sep 20 03:19 UTC (GMT)
-3,496 to signed binary one's complement = ? Sep 20 03:18 UTC (GMT)
4,234,317 to signed binary one's complement = ? Sep 20 03:17 UTC (GMT)
-7,799 to signed binary one's complement = ? Sep 20 03:17 UTC (GMT)
-120,542 to signed binary one's complement = ? Sep 20 03:16 UTC (GMT)
14,123,098 to signed binary one's complement = ? Sep 20 03:15 UTC (GMT)
1,727 to signed binary one's complement = ? Sep 20 03:14 UTC (GMT)
-7,193 to signed binary one's complement = ? Sep 20 03:13 UTC (GMT)
7,767 to signed binary one's complement = ? Sep 20 03:13 UTC (GMT)
1,000,100,100,109,991 to signed binary one's complement = ? Sep 20 03:13 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