Convert 101 110 100 110 184 to a Signed Binary in One's (1's) Complement Representation

How to convert decimal number 101 110 100 110 184(10) to a signed binary in one's (1's) complement representation

What are the steps to convert decimal number
101 110 100 110 184 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;
  • 101 110 100 110 184 ÷ 2 = 50 555 050 055 092 + 0;
  • 50 555 050 055 092 ÷ 2 = 25 277 525 027 546 + 0;
  • 25 277 525 027 546 ÷ 2 = 12 638 762 513 773 + 0;
  • 12 638 762 513 773 ÷ 2 = 6 319 381 256 886 + 1;
  • 6 319 381 256 886 ÷ 2 = 3 159 690 628 443 + 0;
  • 3 159 690 628 443 ÷ 2 = 1 579 845 314 221 + 1;
  • 1 579 845 314 221 ÷ 2 = 789 922 657 110 + 1;
  • 789 922 657 110 ÷ 2 = 394 961 328 555 + 0;
  • 394 961 328 555 ÷ 2 = 197 480 664 277 + 1;
  • 197 480 664 277 ÷ 2 = 98 740 332 138 + 1;
  • 98 740 332 138 ÷ 2 = 49 370 166 069 + 0;
  • 49 370 166 069 ÷ 2 = 24 685 083 034 + 1;
  • 24 685 083 034 ÷ 2 = 12 342 541 517 + 0;
  • 12 342 541 517 ÷ 2 = 6 171 270 758 + 1;
  • 6 171 270 758 ÷ 2 = 3 085 635 379 + 0;
  • 3 085 635 379 ÷ 2 = 1 542 817 689 + 1;
  • 1 542 817 689 ÷ 2 = 771 408 844 + 1;
  • 771 408 844 ÷ 2 = 385 704 422 + 0;
  • 385 704 422 ÷ 2 = 192 852 211 + 0;
  • 192 852 211 ÷ 2 = 96 426 105 + 1;
  • 96 426 105 ÷ 2 = 48 213 052 + 1;
  • 48 213 052 ÷ 2 = 24 106 526 + 0;
  • 24 106 526 ÷ 2 = 12 053 263 + 0;
  • 12 053 263 ÷ 2 = 6 026 631 + 1;
  • 6 026 631 ÷ 2 = 3 013 315 + 1;
  • 3 013 315 ÷ 2 = 1 506 657 + 1;
  • 1 506 657 ÷ 2 = 753 328 + 1;
  • 753 328 ÷ 2 = 376 664 + 0;
  • 376 664 ÷ 2 = 188 332 + 0;
  • 188 332 ÷ 2 = 94 166 + 0;
  • 94 166 ÷ 2 = 47 083 + 0;
  • 47 083 ÷ 2 = 23 541 + 1;
  • 23 541 ÷ 2 = 11 770 + 1;
  • 11 770 ÷ 2 = 5 885 + 0;
  • 5 885 ÷ 2 = 2 942 + 1;
  • 2 942 ÷ 2 = 1 471 + 0;
  • 1 471 ÷ 2 = 735 + 1;
  • 735 ÷ 2 = 367 + 1;
  • 367 ÷ 2 = 183 + 1;
  • 183 ÷ 2 = 91 + 1;
  • 91 ÷ 2 = 45 + 1;
  • 45 ÷ 2 = 22 + 1;
  • 22 ÷ 2 = 11 + 0;
  • 11 ÷ 2 = 5 + 1;
  • 5 ÷ 2 = 2 + 1;
  • 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.

101 110 100 110 184(10) = 101 1011 1111 0101 1000 0111 1001 1001 1010 1011 0110 1000(2)

3. Determine the signed binary number bit length:

  • The base 2 number's actual length, in bits: 47.

  • 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, 47,

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 101 110 100 110 184(10) converted to signed binary in one's complement representation:

101 110 100 110 184(10) = 0000 0000 0000 0000 0101 1011 1111 0101 1000 0111 1001 1001 1010 1011 0110 1000

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