Two's Complement: Integer ↗ Binary: 1 110 000 010 110 024 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 1 110 000 010 110 024(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;
  • 1 110 000 010 110 024 ÷ 2 = 555 000 005 055 012 + 0;
  • 555 000 005 055 012 ÷ 2 = 277 500 002 527 506 + 0;
  • 277 500 002 527 506 ÷ 2 = 138 750 001 263 753 + 0;
  • 138 750 001 263 753 ÷ 2 = 69 375 000 631 876 + 1;
  • 69 375 000 631 876 ÷ 2 = 34 687 500 315 938 + 0;
  • 34 687 500 315 938 ÷ 2 = 17 343 750 157 969 + 0;
  • 17 343 750 157 969 ÷ 2 = 8 671 875 078 984 + 1;
  • 8 671 875 078 984 ÷ 2 = 4 335 937 539 492 + 0;
  • 4 335 937 539 492 ÷ 2 = 2 167 968 769 746 + 0;
  • 2 167 968 769 746 ÷ 2 = 1 083 984 384 873 + 0;
  • 1 083 984 384 873 ÷ 2 = 541 992 192 436 + 1;
  • 541 992 192 436 ÷ 2 = 270 996 096 218 + 0;
  • 270 996 096 218 ÷ 2 = 135 498 048 109 + 0;
  • 135 498 048 109 ÷ 2 = 67 749 024 054 + 1;
  • 67 749 024 054 ÷ 2 = 33 874 512 027 + 0;
  • 33 874 512 027 ÷ 2 = 16 937 256 013 + 1;
  • 16 937 256 013 ÷ 2 = 8 468 628 006 + 1;
  • 8 468 628 006 ÷ 2 = 4 234 314 003 + 0;
  • 4 234 314 003 ÷ 2 = 2 117 157 001 + 1;
  • 2 117 157 001 ÷ 2 = 1 058 578 500 + 1;
  • 1 058 578 500 ÷ 2 = 529 289 250 + 0;
  • 529 289 250 ÷ 2 = 264 644 625 + 0;
  • 264 644 625 ÷ 2 = 132 322 312 + 1;
  • 132 322 312 ÷ 2 = 66 161 156 + 0;
  • 66 161 156 ÷ 2 = 33 080 578 + 0;
  • 33 080 578 ÷ 2 = 16 540 289 + 0;
  • 16 540 289 ÷ 2 = 8 270 144 + 1;
  • 8 270 144 ÷ 2 = 4 135 072 + 0;
  • 4 135 072 ÷ 2 = 2 067 536 + 0;
  • 2 067 536 ÷ 2 = 1 033 768 + 0;
  • 1 033 768 ÷ 2 = 516 884 + 0;
  • 516 884 ÷ 2 = 258 442 + 0;
  • 258 442 ÷ 2 = 129 221 + 0;
  • 129 221 ÷ 2 = 64 610 + 1;
  • 64 610 ÷ 2 = 32 305 + 0;
  • 32 305 ÷ 2 = 16 152 + 1;
  • 16 152 ÷ 2 = 8 076 + 0;
  • 8 076 ÷ 2 = 4 038 + 0;
  • 4 038 ÷ 2 = 2 019 + 0;
  • 2 019 ÷ 2 = 1 009 + 1;
  • 1 009 ÷ 2 = 504 + 1;
  • 504 ÷ 2 = 252 + 0;
  • 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.


1 110 000 010 110 024(10) = 11 1111 0001 1000 1010 0000 0100 0100 1101 1010 0100 0100 1000(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 1 110 000 010 110 024(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:

1 110 000 010 110 024(10) = 0000 0000 0000 0011 1111 0001 1000 1010 0000 0100 0100 1101 1010 0100 0100 1000

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 1 110 000 010 110 023 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 1 110 000 010 110 025 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