Convert 167 211 709 540 492 to a Signed Binary in One's (1's) Complement Representation

How to convert decimal number 167 211 709 540 492(10) to a signed binary in one's (1's) complement representation

What are the steps to convert decimal number
167 211 709 540 492 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;
  • 167 211 709 540 492 ÷ 2 = 83 605 854 770 246 + 0;
  • 83 605 854 770 246 ÷ 2 = 41 802 927 385 123 + 0;
  • 41 802 927 385 123 ÷ 2 = 20 901 463 692 561 + 1;
  • 20 901 463 692 561 ÷ 2 = 10 450 731 846 280 + 1;
  • 10 450 731 846 280 ÷ 2 = 5 225 365 923 140 + 0;
  • 5 225 365 923 140 ÷ 2 = 2 612 682 961 570 + 0;
  • 2 612 682 961 570 ÷ 2 = 1 306 341 480 785 + 0;
  • 1 306 341 480 785 ÷ 2 = 653 170 740 392 + 1;
  • 653 170 740 392 ÷ 2 = 326 585 370 196 + 0;
  • 326 585 370 196 ÷ 2 = 163 292 685 098 + 0;
  • 163 292 685 098 ÷ 2 = 81 646 342 549 + 0;
  • 81 646 342 549 ÷ 2 = 40 823 171 274 + 1;
  • 40 823 171 274 ÷ 2 = 20 411 585 637 + 0;
  • 20 411 585 637 ÷ 2 = 10 205 792 818 + 1;
  • 10 205 792 818 ÷ 2 = 5 102 896 409 + 0;
  • 5 102 896 409 ÷ 2 = 2 551 448 204 + 1;
  • 2 551 448 204 ÷ 2 = 1 275 724 102 + 0;
  • 1 275 724 102 ÷ 2 = 637 862 051 + 0;
  • 637 862 051 ÷ 2 = 318 931 025 + 1;
  • 318 931 025 ÷ 2 = 159 465 512 + 1;
  • 159 465 512 ÷ 2 = 79 732 756 + 0;
  • 79 732 756 ÷ 2 = 39 866 378 + 0;
  • 39 866 378 ÷ 2 = 19 933 189 + 0;
  • 19 933 189 ÷ 2 = 9 966 594 + 1;
  • 9 966 594 ÷ 2 = 4 983 297 + 0;
  • 4 983 297 ÷ 2 = 2 491 648 + 1;
  • 2 491 648 ÷ 2 = 1 245 824 + 0;
  • 1 245 824 ÷ 2 = 622 912 + 0;
  • 622 912 ÷ 2 = 311 456 + 0;
  • 311 456 ÷ 2 = 155 728 + 0;
  • 155 728 ÷ 2 = 77 864 + 0;
  • 77 864 ÷ 2 = 38 932 + 0;
  • 38 932 ÷ 2 = 19 466 + 0;
  • 19 466 ÷ 2 = 9 733 + 0;
  • 9 733 ÷ 2 = 4 866 + 1;
  • 4 866 ÷ 2 = 2 433 + 0;
  • 2 433 ÷ 2 = 1 216 + 1;
  • 1 216 ÷ 2 = 608 + 0;
  • 608 ÷ 2 = 304 + 0;
  • 304 ÷ 2 = 152 + 0;
  • 152 ÷ 2 = 76 + 0;
  • 76 ÷ 2 = 38 + 0;
  • 38 ÷ 2 = 19 + 0;
  • 19 ÷ 2 = 9 + 1;
  • 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.

167 211 709 540 492(10) = 1001 1000 0001 0100 0000 0010 1000 1100 1010 1000 1000 1100(2)

3. Determine the signed binary number bit length:

  • The base 2 number's actual length, in bits: 48.

  • 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, 48,

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 167 211 709 540 492(10) converted to signed binary in one's complement representation:

167 211 709 540 492(10) = 0000 0000 0000 0000 1001 1000 0001 0100 0000 0010 1000 1100 1010 1000 1000 1100

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