Convert 10 011 011 000 467 to a Signed Binary in One's (1's) Complement Representation

How to convert decimal number 10 011 011 000 467(10) to a signed binary in one's (1's) complement representation

What are the steps to convert decimal number
10 011 011 000 467 to a signed binary in one's (1's) complement representation?

  • A signed integer, written in base ten, or a decimal system number, is a number written using the digits 0 through 9 and the sign, which can be positive (+) or negative (-). If positive, the sign is usually not written. A number written in base two, or binary, is a number written using only the digits 0 and 1.

1. Divide the number repeatedly by 2:

Keep track of each remainder.

Stop when you get a quotient that is equal to zero.


  • division = quotient + remainder;
  • 10 011 011 000 467 ÷ 2 = 5 005 505 500 233 + 1;
  • 5 005 505 500 233 ÷ 2 = 2 502 752 750 116 + 1;
  • 2 502 752 750 116 ÷ 2 = 1 251 376 375 058 + 0;
  • 1 251 376 375 058 ÷ 2 = 625 688 187 529 + 0;
  • 625 688 187 529 ÷ 2 = 312 844 093 764 + 1;
  • 312 844 093 764 ÷ 2 = 156 422 046 882 + 0;
  • 156 422 046 882 ÷ 2 = 78 211 023 441 + 0;
  • 78 211 023 441 ÷ 2 = 39 105 511 720 + 1;
  • 39 105 511 720 ÷ 2 = 19 552 755 860 + 0;
  • 19 552 755 860 ÷ 2 = 9 776 377 930 + 0;
  • 9 776 377 930 ÷ 2 = 4 888 188 965 + 0;
  • 4 888 188 965 ÷ 2 = 2 444 094 482 + 1;
  • 2 444 094 482 ÷ 2 = 1 222 047 241 + 0;
  • 1 222 047 241 ÷ 2 = 611 023 620 + 1;
  • 611 023 620 ÷ 2 = 305 511 810 + 0;
  • 305 511 810 ÷ 2 = 152 755 905 + 0;
  • 152 755 905 ÷ 2 = 76 377 952 + 1;
  • 76 377 952 ÷ 2 = 38 188 976 + 0;
  • 38 188 976 ÷ 2 = 19 094 488 + 0;
  • 19 094 488 ÷ 2 = 9 547 244 + 0;
  • 9 547 244 ÷ 2 = 4 773 622 + 0;
  • 4 773 622 ÷ 2 = 2 386 811 + 0;
  • 2 386 811 ÷ 2 = 1 193 405 + 1;
  • 1 193 405 ÷ 2 = 596 702 + 1;
  • 596 702 ÷ 2 = 298 351 + 0;
  • 298 351 ÷ 2 = 149 175 + 1;
  • 149 175 ÷ 2 = 74 587 + 1;
  • 74 587 ÷ 2 = 37 293 + 1;
  • 37 293 ÷ 2 = 18 646 + 1;
  • 18 646 ÷ 2 = 9 323 + 0;
  • 9 323 ÷ 2 = 4 661 + 1;
  • 4 661 ÷ 2 = 2 330 + 1;
  • 2 330 ÷ 2 = 1 165 + 0;
  • 1 165 ÷ 2 = 582 + 1;
  • 582 ÷ 2 = 291 + 0;
  • 291 ÷ 2 = 145 + 1;
  • 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;

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

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

10 011 011 000 467(10) = 1001 0001 1010 1101 1110 1100 0001 0010 1000 1001 0011(2)

3. Determine the signed binary number bit length:

  • The base 2 number's actual length, in bits: 44.

  • 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; ...
  • The first bit (the leftmost) indicates the sign:
  • 0 = positive integer number, 1 = negative integer number

The least number that is:

1) a power of 2

2) and is larger than the actual length, 44,

3) so that the first bit (leftmost) could be zero
(we deal with a positive number at this moment)

=== is: 64.


4. Get the 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.


Decimal Number 10 011 011 000 467(10) converted to signed binary in one's complement representation:

10 011 011 000 467(10) = 0000 0000 0000 0000 0000 1001 0001 1010 1101 1110 1100 0001 0010 1000 1001 0011

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

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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