One's Complement: Integer ↗ Binary: 1 001 101 000 088 Convert the Integer Number to a Signed Binary in One's Complement Representation. Write the Base Ten Decimal System Number as a Binary Code (Written in Base Two)

Signed integer number 1 001 101 000 088(10) converted and written as a signed binary in one's complement representation (base 2) = ?

1. Divide the number repeatedly by 2:

Keep track of each remainder.

We stop when we get a quotient that is equal to zero.


  • division = quotient + remainder;
  • 1 001 101 000 088 ÷ 2 = 500 550 500 044 + 0;
  • 500 550 500 044 ÷ 2 = 250 275 250 022 + 0;
  • 250 275 250 022 ÷ 2 = 125 137 625 011 + 0;
  • 125 137 625 011 ÷ 2 = 62 568 812 505 + 1;
  • 62 568 812 505 ÷ 2 = 31 284 406 252 + 1;
  • 31 284 406 252 ÷ 2 = 15 642 203 126 + 0;
  • 15 642 203 126 ÷ 2 = 7 821 101 563 + 0;
  • 7 821 101 563 ÷ 2 = 3 910 550 781 + 1;
  • 3 910 550 781 ÷ 2 = 1 955 275 390 + 1;
  • 1 955 275 390 ÷ 2 = 977 637 695 + 0;
  • 977 637 695 ÷ 2 = 488 818 847 + 1;
  • 488 818 847 ÷ 2 = 244 409 423 + 1;
  • 244 409 423 ÷ 2 = 122 204 711 + 1;
  • 122 204 711 ÷ 2 = 61 102 355 + 1;
  • 61 102 355 ÷ 2 = 30 551 177 + 1;
  • 30 551 177 ÷ 2 = 15 275 588 + 1;
  • 15 275 588 ÷ 2 = 7 637 794 + 0;
  • 7 637 794 ÷ 2 = 3 818 897 + 0;
  • 3 818 897 ÷ 2 = 1 909 448 + 1;
  • 1 909 448 ÷ 2 = 954 724 + 0;
  • 954 724 ÷ 2 = 477 362 + 0;
  • 477 362 ÷ 2 = 238 681 + 0;
  • 238 681 ÷ 2 = 119 340 + 1;
  • 119 340 ÷ 2 = 59 670 + 0;
  • 59 670 ÷ 2 = 29 835 + 0;
  • 29 835 ÷ 2 = 14 917 + 1;
  • 14 917 ÷ 2 = 7 458 + 1;
  • 7 458 ÷ 2 = 3 729 + 0;
  • 3 729 ÷ 2 = 1 864 + 1;
  • 1 864 ÷ 2 = 932 + 0;
  • 932 ÷ 2 = 466 + 0;
  • 466 ÷ 2 = 233 + 0;
  • 233 ÷ 2 = 116 + 1;
  • 116 ÷ 2 = 58 + 0;
  • 58 ÷ 2 = 29 + 0;
  • 29 ÷ 2 = 14 + 1;
  • 14 ÷ 2 = 7 + 0;
  • 7 ÷ 2 = 3 + 1;
  • 3 ÷ 2 = 1 + 1;
  • 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.


1 001 101 000 088(10) = 1110 1001 0001 0110 0100 0100 1111 1101 1001 1000(2)


3. Determine the signed binary number bit length:

The base 2 number's actual length, in bits: 40.

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, 40,

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.


Number 1 001 101 000 088(10), a signed integer number (with sign), converted from decimal system (from base 10) and written as a signed binary in one's complement representation:

1 001 101 000 088(10) = 0000 0000 0000 0000 0000 0000 1110 1001 0001 0110 0100 0100 1111 1101 1001 1000

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

More operations on signed integers written as signed binary numbers in one's complement representation:

» Signed integer number 1 001 101 000 087 converted from decimal system (from base 10) and written as a signed binary in one's complement representation (written in base 2) = ?

» Signed integer number 1 001 101 000 089 converted from decimal system (from base 10) and written as a signed binary in one's complement representation (written in base 2) = ?

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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