Two's Complement: Integer ↗ Binary: 11 000 110 111 000 092 Convert the Integer Number to a Signed Binary in Two's Complement Representation. Write the Base Ten Decimal System Number as a Binary Code (Written in Base Two)

Signed integer number 11 000 110 111 000 092(10) converted and written as a signed binary in two'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;
  • 11 000 110 111 000 092 ÷ 2 = 5 500 055 055 500 046 + 0;
  • 5 500 055 055 500 046 ÷ 2 = 2 750 027 527 750 023 + 0;
  • 2 750 027 527 750 023 ÷ 2 = 1 375 013 763 875 011 + 1;
  • 1 375 013 763 875 011 ÷ 2 = 687 506 881 937 505 + 1;
  • 687 506 881 937 505 ÷ 2 = 343 753 440 968 752 + 1;
  • 343 753 440 968 752 ÷ 2 = 171 876 720 484 376 + 0;
  • 171 876 720 484 376 ÷ 2 = 85 938 360 242 188 + 0;
  • 85 938 360 242 188 ÷ 2 = 42 969 180 121 094 + 0;
  • 42 969 180 121 094 ÷ 2 = 21 484 590 060 547 + 0;
  • 21 484 590 060 547 ÷ 2 = 10 742 295 030 273 + 1;
  • 10 742 295 030 273 ÷ 2 = 5 371 147 515 136 + 1;
  • 5 371 147 515 136 ÷ 2 = 2 685 573 757 568 + 0;
  • 2 685 573 757 568 ÷ 2 = 1 342 786 878 784 + 0;
  • 1 342 786 878 784 ÷ 2 = 671 393 439 392 + 0;
  • 671 393 439 392 ÷ 2 = 335 696 719 696 + 0;
  • 335 696 719 696 ÷ 2 = 167 848 359 848 + 0;
  • 167 848 359 848 ÷ 2 = 83 924 179 924 + 0;
  • 83 924 179 924 ÷ 2 = 41 962 089 962 + 0;
  • 41 962 089 962 ÷ 2 = 20 981 044 981 + 0;
  • 20 981 044 981 ÷ 2 = 10 490 522 490 + 1;
  • 10 490 522 490 ÷ 2 = 5 245 261 245 + 0;
  • 5 245 261 245 ÷ 2 = 2 622 630 622 + 1;
  • 2 622 630 622 ÷ 2 = 1 311 315 311 + 0;
  • 1 311 315 311 ÷ 2 = 655 657 655 + 1;
  • 655 657 655 ÷ 2 = 327 828 827 + 1;
  • 327 828 827 ÷ 2 = 163 914 413 + 1;
  • 163 914 413 ÷ 2 = 81 957 206 + 1;
  • 81 957 206 ÷ 2 = 40 978 603 + 0;
  • 40 978 603 ÷ 2 = 20 489 301 + 1;
  • 20 489 301 ÷ 2 = 10 244 650 + 1;
  • 10 244 650 ÷ 2 = 5 122 325 + 0;
  • 5 122 325 ÷ 2 = 2 561 162 + 1;
  • 2 561 162 ÷ 2 = 1 280 581 + 0;
  • 1 280 581 ÷ 2 = 640 290 + 1;
  • 640 290 ÷ 2 = 320 145 + 0;
  • 320 145 ÷ 2 = 160 072 + 1;
  • 160 072 ÷ 2 = 80 036 + 0;
  • 80 036 ÷ 2 = 40 018 + 0;
  • 40 018 ÷ 2 = 20 009 + 0;
  • 20 009 ÷ 2 = 10 004 + 1;
  • 10 004 ÷ 2 = 5 002 + 0;
  • 5 002 ÷ 2 = 2 501 + 0;
  • 2 501 ÷ 2 = 1 250 + 1;
  • 1 250 ÷ 2 = 625 + 0;
  • 625 ÷ 2 = 312 + 1;
  • 312 ÷ 2 = 156 + 0;
  • 156 ÷ 2 = 78 + 0;
  • 78 ÷ 2 = 39 + 0;
  • 39 ÷ 2 = 19 + 1;
  • 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.


11 000 110 111 000 092(10) = 10 0111 0001 0100 1000 1010 1011 0111 1010 1000 0000 0110 0001 1100(2)


3. Determine the signed binary number bit length:

The base 2 number's actual length, in bits: 54.

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, 54,

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 11 000 110 111 000 092(10), a signed integer number (with sign), converted from decimal system (from base 10) and written as a signed binary in two's complement representation:

11 000 110 111 000 092(10) = 0000 0000 0010 0111 0001 0100 1000 1010 1011 0111 1010 1000 0000 0110 0001 1100

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

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

» Signed integer number 11 000 110 111 000 091 converted from decimal system (from base 10) and written as a signed binary in two's complement representation (written in base 2) = ?

» Signed integer number 11 000 110 111 000 093 converted from decimal system (from base 10) and written as a signed binary in two's complement representation (written in base 2) = ?

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How to convert signed integers from decimal system to signed binary in two's complement representation

Follow the steps below to convert a signed base 10 integer number to signed binary in two'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, keeping track of each remainder, until we get a quotient that is 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, add extra bits on 0 in front (to the left) of the base 2 number above, up to the required length, so that the first bit (the leftmost) will 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 1s and all 1 bits with 0s (reversing the digits).
  • 6. To get the negative integer number, in signed binary two's complement representation, add 1 to the number above.

Example: convert the negative number -60 from the decimal system (base ten) to signed binary in two's complement:

  • 1. Start with the positive version of the number: |-60| = 60
  • 2. Divide repeatedly 60 by 2, keeping track of each remainder:
    • division = quotient + remainder
    • 60 ÷ 2 = 30 + 0
    • 30 ÷ 2 = 15 + 0
    • 15 ÷ 2 = 7 + 1
    • 7 ÷ 2 = 3 + 1
    • 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:
    60(10) = 11 1100(2)
  • 4. Bit length of base 2 representation number is 6, so the positive binary computer representation of a signed binary will take in this particular case 8 bits (the least power of 2 larger than 6) - add extra 0 digits in front of the base 2 number, up to the required length:
    60(10) = 0011 1100(2)
  • 5. To get the negative integer number representation in signed binary one's complement, replace all the 0 bits with 1s and all 1 bits with 0s (reversing the digits):
    !(0011 1100) = 1100 0011
  • 6. To get the negative integer number, signed binary in two's complement representation, add 1 to the number above:
    -60(10) = 1100 0011 + 1 = 1100 0100
  • Number -60(10), signed integer, converted from decimal system (base 10) to signed binary two's complement representation = 1100 0100