Convert 101 101 109 999 621 to a Signed Binary in One's (1's) Complement Representation

How to convert decimal number 101 101 109 999 621(10) to a signed binary in one's (1's) complement representation

What are the steps to convert decimal number
101 101 109 999 621 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;
  • 101 101 109 999 621 ÷ 2 = 50 550 554 999 810 + 1;
  • 50 550 554 999 810 ÷ 2 = 25 275 277 499 905 + 0;
  • 25 275 277 499 905 ÷ 2 = 12 637 638 749 952 + 1;
  • 12 637 638 749 952 ÷ 2 = 6 318 819 374 976 + 0;
  • 6 318 819 374 976 ÷ 2 = 3 159 409 687 488 + 0;
  • 3 159 409 687 488 ÷ 2 = 1 579 704 843 744 + 0;
  • 1 579 704 843 744 ÷ 2 = 789 852 421 872 + 0;
  • 789 852 421 872 ÷ 2 = 394 926 210 936 + 0;
  • 394 926 210 936 ÷ 2 = 197 463 105 468 + 0;
  • 197 463 105 468 ÷ 2 = 98 731 552 734 + 0;
  • 98 731 552 734 ÷ 2 = 49 365 776 367 + 0;
  • 49 365 776 367 ÷ 2 = 24 682 888 183 + 1;
  • 24 682 888 183 ÷ 2 = 12 341 444 091 + 1;
  • 12 341 444 091 ÷ 2 = 6 170 722 045 + 1;
  • 6 170 722 045 ÷ 2 = 3 085 361 022 + 1;
  • 3 085 361 022 ÷ 2 = 1 542 680 511 + 0;
  • 1 542 680 511 ÷ 2 = 771 340 255 + 1;
  • 771 340 255 ÷ 2 = 385 670 127 + 1;
  • 385 670 127 ÷ 2 = 192 835 063 + 1;
  • 192 835 063 ÷ 2 = 96 417 531 + 1;
  • 96 417 531 ÷ 2 = 48 208 765 + 1;
  • 48 208 765 ÷ 2 = 24 104 382 + 1;
  • 24 104 382 ÷ 2 = 12 052 191 + 0;
  • 12 052 191 ÷ 2 = 6 026 095 + 1;
  • 6 026 095 ÷ 2 = 3 013 047 + 1;
  • 3 013 047 ÷ 2 = 1 506 523 + 1;
  • 1 506 523 ÷ 2 = 753 261 + 1;
  • 753 261 ÷ 2 = 376 630 + 1;
  • 376 630 ÷ 2 = 188 315 + 0;
  • 188 315 ÷ 2 = 94 157 + 1;
  • 94 157 ÷ 2 = 47 078 + 1;
  • 47 078 ÷ 2 = 23 539 + 0;
  • 23 539 ÷ 2 = 11 769 + 1;
  • 11 769 ÷ 2 = 5 884 + 1;
  • 5 884 ÷ 2 = 2 942 + 0;
  • 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.

101 101 109 999 621(10) = 101 1011 1111 0011 0110 1111 1011 1111 0111 1000 0000 0101(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 101 101 109 999 621(10) converted to signed binary in one's complement representation:

101 101 109 999 621(10) = 0000 0000 0000 0000 0101 1011 1111 0011 0110 1111 1011 1111 0111 1000 0000 0101

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