Convert Decimal 10 110 101 010 672 to Signed Binary in One's (1's) Complement Representation

How to convert decimal number 10 110 101 010 672(10) to a signed binary in one's (1's) complement representation

What are the steps to convert decimal number
10 110 101 010 672 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;
  • 10 110 101 010 672 ÷ 2 = 5 055 050 505 336 + 0;
  • 5 055 050 505 336 ÷ 2 = 2 527 525 252 668 + 0;
  • 2 527 525 252 668 ÷ 2 = 1 263 762 626 334 + 0;
  • 1 263 762 626 334 ÷ 2 = 631 881 313 167 + 0;
  • 631 881 313 167 ÷ 2 = 315 940 656 583 + 1;
  • 315 940 656 583 ÷ 2 = 157 970 328 291 + 1;
  • 157 970 328 291 ÷ 2 = 78 985 164 145 + 1;
  • 78 985 164 145 ÷ 2 = 39 492 582 072 + 1;
  • 39 492 582 072 ÷ 2 = 19 746 291 036 + 0;
  • 19 746 291 036 ÷ 2 = 9 873 145 518 + 0;
  • 9 873 145 518 ÷ 2 = 4 936 572 759 + 0;
  • 4 936 572 759 ÷ 2 = 2 468 286 379 + 1;
  • 2 468 286 379 ÷ 2 = 1 234 143 189 + 1;
  • 1 234 143 189 ÷ 2 = 617 071 594 + 1;
  • 617 071 594 ÷ 2 = 308 535 797 + 0;
  • 308 535 797 ÷ 2 = 154 267 898 + 1;
  • 154 267 898 ÷ 2 = 77 133 949 + 0;
  • 77 133 949 ÷ 2 = 38 566 974 + 1;
  • 38 566 974 ÷ 2 = 19 283 487 + 0;
  • 19 283 487 ÷ 2 = 9 641 743 + 1;
  • 9 641 743 ÷ 2 = 4 820 871 + 1;
  • 4 820 871 ÷ 2 = 2 410 435 + 1;
  • 2 410 435 ÷ 2 = 1 205 217 + 1;
  • 1 205 217 ÷ 2 = 602 608 + 1;
  • 602 608 ÷ 2 = 301 304 + 0;
  • 301 304 ÷ 2 = 150 652 + 0;
  • 150 652 ÷ 2 = 75 326 + 0;
  • 75 326 ÷ 2 = 37 663 + 0;
  • 37 663 ÷ 2 = 18 831 + 1;
  • 18 831 ÷ 2 = 9 415 + 1;
  • 9 415 ÷ 2 = 4 707 + 1;
  • 4 707 ÷ 2 = 2 353 + 1;
  • 2 353 ÷ 2 = 1 176 + 1;
  • 1 176 ÷ 2 = 588 + 0;
  • 588 ÷ 2 = 294 + 0;
  • 294 ÷ 2 = 147 + 0;
  • 147 ÷ 2 = 73 + 1;
  • 73 ÷ 2 = 36 + 1;
  • 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.

10 110 101 010 672(10) = 1001 0011 0001 1111 0000 1111 1010 1011 1000 1111 0000(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 10 110 101 010 672(10) converted to signed binary in one's complement representation:

10 110 101 010 672(10) = 0000 0000 0000 0000 0000 1001 0011 0001 1111 0000 1111 1010 1011 1000 1111 0000

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