Convert 974 294 967 268 to a signed binary in one's complement representation, from a base 10 decimal system signed integer number

974 294 967 268(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;
  • 974 294 967 268 ÷ 2 = 487 147 483 634 + 0;
  • 487 147 483 634 ÷ 2 = 243 573 741 817 + 0;
  • 243 573 741 817 ÷ 2 = 121 786 870 908 + 1;
  • 121 786 870 908 ÷ 2 = 60 893 435 454 + 0;
  • 60 893 435 454 ÷ 2 = 30 446 717 727 + 0;
  • 30 446 717 727 ÷ 2 = 15 223 358 863 + 1;
  • 15 223 358 863 ÷ 2 = 7 611 679 431 + 1;
  • 7 611 679 431 ÷ 2 = 3 805 839 715 + 1;
  • 3 805 839 715 ÷ 2 = 1 902 919 857 + 1;
  • 1 902 919 857 ÷ 2 = 951 459 928 + 1;
  • 951 459 928 ÷ 2 = 475 729 964 + 0;
  • 475 729 964 ÷ 2 = 237 864 982 + 0;
  • 237 864 982 ÷ 2 = 118 932 491 + 0;
  • 118 932 491 ÷ 2 = 59 466 245 + 1;
  • 59 466 245 ÷ 2 = 29 733 122 + 1;
  • 29 733 122 ÷ 2 = 14 866 561 + 0;
  • 14 866 561 ÷ 2 = 7 433 280 + 1;
  • 7 433 280 ÷ 2 = 3 716 640 + 0;
  • 3 716 640 ÷ 2 = 1 858 320 + 0;
  • 1 858 320 ÷ 2 = 929 160 + 0;
  • 929 160 ÷ 2 = 464 580 + 0;
  • 464 580 ÷ 2 = 232 290 + 0;
  • 232 290 ÷ 2 = 116 145 + 0;
  • 116 145 ÷ 2 = 58 072 + 1;
  • 58 072 ÷ 2 = 29 036 + 0;
  • 29 036 ÷ 2 = 14 518 + 0;
  • 14 518 ÷ 2 = 7 259 + 0;
  • 7 259 ÷ 2 = 3 629 + 1;
  • 3 629 ÷ 2 = 1 814 + 1;
  • 1 814 ÷ 2 = 907 + 0;
  • 907 ÷ 2 = 453 + 1;
  • 453 ÷ 2 = 226 + 1;
  • 226 ÷ 2 = 113 + 0;
  • 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.

974 294 967 268(10) = 1110 0010 1101 1000 1000 0001 0110 0011 1110 0100(2)


3. Determine the signed binary number bit length:

The base 2 number's actual length, in bits: 40.

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, 40,


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:

974 294 967 268(10) = 0000 0000 0000 0000 0000 0000 1110 0010 1101 1000 1000 0001 0110 0011 1110 0100


Number 974 294 967 268, a signed integer, converted from decimal system (base 10) to a signed binary one's complement representation:

974 294 967 268(10) = 0000 0000 0000 0000 0000 0000 1110 0010 1101 1000 1000 0001 0110 0011 1110 0100

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


More operations of this kind:

974 294 967 267 = ? | 974 294 967 269 = ?


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

974,294,967,268 to signed binary one's complement = ? Jul 24 10:31 UTC (GMT)
1,018 to signed binary one's complement = ? Jul 24 10:31 UTC (GMT)
1,011,029 to signed binary one's complement = ? Jul 24 10:31 UTC (GMT)
111,111,088 to signed binary one's complement = ? Jul 24 10:30 UTC (GMT)
-4,097 to signed binary one's complement = ? Jul 24 10:30 UTC (GMT)
-39 to signed binary one's complement = ? Jul 24 10:30 UTC (GMT)
10,110,104 to signed binary one's complement = ? Jul 24 10:30 UTC (GMT)
10,010,119 to signed binary one's complement = ? Jul 24 10:30 UTC (GMT)
-1,000,012 to signed binary one's complement = ? Jul 24 10:29 UTC (GMT)
-55 to signed binary one's complement = ? Jul 24 10:29 UTC (GMT)
178 to signed binary one's complement = ? Jul 24 10:28 UTC (GMT)
-11,944 to signed binary one's complement = ? Jul 24 10:28 UTC (GMT)
-20,012 to signed binary one's complement = ? Jul 24 10:28 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