Two's Complement: Integer ↗ Binary: 1 111 111 100 110 994 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 1 111 111 100 110 994(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;
  • 1 111 111 100 110 994 ÷ 2 = 555 555 550 055 497 + 0;
  • 555 555 550 055 497 ÷ 2 = 277 777 775 027 748 + 1;
  • 277 777 775 027 748 ÷ 2 = 138 888 887 513 874 + 0;
  • 138 888 887 513 874 ÷ 2 = 69 444 443 756 937 + 0;
  • 69 444 443 756 937 ÷ 2 = 34 722 221 878 468 + 1;
  • 34 722 221 878 468 ÷ 2 = 17 361 110 939 234 + 0;
  • 17 361 110 939 234 ÷ 2 = 8 680 555 469 617 + 0;
  • 8 680 555 469 617 ÷ 2 = 4 340 277 734 808 + 1;
  • 4 340 277 734 808 ÷ 2 = 2 170 138 867 404 + 0;
  • 2 170 138 867 404 ÷ 2 = 1 085 069 433 702 + 0;
  • 1 085 069 433 702 ÷ 2 = 542 534 716 851 + 0;
  • 542 534 716 851 ÷ 2 = 271 267 358 425 + 1;
  • 271 267 358 425 ÷ 2 = 135 633 679 212 + 1;
  • 135 633 679 212 ÷ 2 = 67 816 839 606 + 0;
  • 67 816 839 606 ÷ 2 = 33 908 419 803 + 0;
  • 33 908 419 803 ÷ 2 = 16 954 209 901 + 1;
  • 16 954 209 901 ÷ 2 = 8 477 104 950 + 1;
  • 8 477 104 950 ÷ 2 = 4 238 552 475 + 0;
  • 4 238 552 475 ÷ 2 = 2 119 276 237 + 1;
  • 2 119 276 237 ÷ 2 = 1 059 638 118 + 1;
  • 1 059 638 118 ÷ 2 = 529 819 059 + 0;
  • 529 819 059 ÷ 2 = 264 909 529 + 1;
  • 264 909 529 ÷ 2 = 132 454 764 + 1;
  • 132 454 764 ÷ 2 = 66 227 382 + 0;
  • 66 227 382 ÷ 2 = 33 113 691 + 0;
  • 33 113 691 ÷ 2 = 16 556 845 + 1;
  • 16 556 845 ÷ 2 = 8 278 422 + 1;
  • 8 278 422 ÷ 2 = 4 139 211 + 0;
  • 4 139 211 ÷ 2 = 2 069 605 + 1;
  • 2 069 605 ÷ 2 = 1 034 802 + 1;
  • 1 034 802 ÷ 2 = 517 401 + 0;
  • 517 401 ÷ 2 = 258 700 + 1;
  • 258 700 ÷ 2 = 129 350 + 0;
  • 129 350 ÷ 2 = 64 675 + 0;
  • 64 675 ÷ 2 = 32 337 + 1;
  • 32 337 ÷ 2 = 16 168 + 1;
  • 16 168 ÷ 2 = 8 084 + 0;
  • 8 084 ÷ 2 = 4 042 + 0;
  • 4 042 ÷ 2 = 2 021 + 0;
  • 2 021 ÷ 2 = 1 010 + 1;
  • 1 010 ÷ 2 = 505 + 0;
  • 505 ÷ 2 = 252 + 1;
  • 252 ÷ 2 = 126 + 0;
  • 126 ÷ 2 = 63 + 0;
  • 63 ÷ 2 = 31 + 1;
  • 31 ÷ 2 = 15 + 1;
  • 15 ÷ 2 = 7 + 1;
  • 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.


1 111 111 100 110 994(10) = 11 1111 0010 1000 1100 1011 0110 0110 1101 1001 1000 1001 0010(2)


3. Determine the signed binary number bit length:

The base 2 number's actual length, in bits: 50.

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, 50,

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 1 111 111 100 110 994(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:

1 111 111 100 110 994(10) = 0000 0000 0000 0011 1111 0010 1000 1100 1011 0110 0110 1101 1001 1000 1001 0010

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 1 111 111 100 110 993 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 1 111 111 100 110 995 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