Two's Complement: Integer ↗ Binary: -92 233 720 368 548 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 -92 233 720 368 548(10) converted and written as a signed binary in two's complement representation (base 2) = ?

1. Start with the positive version of the number:

|-92 233 720 368 548| = 92 233 720 368 548

2. 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;
  • 92 233 720 368 548 ÷ 2 = 46 116 860 184 274 + 0;
  • 46 116 860 184 274 ÷ 2 = 23 058 430 092 137 + 0;
  • 23 058 430 092 137 ÷ 2 = 11 529 215 046 068 + 1;
  • 11 529 215 046 068 ÷ 2 = 5 764 607 523 034 + 0;
  • 5 764 607 523 034 ÷ 2 = 2 882 303 761 517 + 0;
  • 2 882 303 761 517 ÷ 2 = 1 441 151 880 758 + 1;
  • 1 441 151 880 758 ÷ 2 = 720 575 940 379 + 0;
  • 720 575 940 379 ÷ 2 = 360 287 970 189 + 1;
  • 360 287 970 189 ÷ 2 = 180 143 985 094 + 1;
  • 180 143 985 094 ÷ 2 = 90 071 992 547 + 0;
  • 90 071 992 547 ÷ 2 = 45 035 996 273 + 1;
  • 45 035 996 273 ÷ 2 = 22 517 998 136 + 1;
  • 22 517 998 136 ÷ 2 = 11 258 999 068 + 0;
  • 11 258 999 068 ÷ 2 = 5 629 499 534 + 0;
  • 5 629 499 534 ÷ 2 = 2 814 749 767 + 0;
  • 2 814 749 767 ÷ 2 = 1 407 374 883 + 1;
  • 1 407 374 883 ÷ 2 = 703 687 441 + 1;
  • 703 687 441 ÷ 2 = 351 843 720 + 1;
  • 351 843 720 ÷ 2 = 175 921 860 + 0;
  • 175 921 860 ÷ 2 = 87 960 930 + 0;
  • 87 960 930 ÷ 2 = 43 980 465 + 0;
  • 43 980 465 ÷ 2 = 21 990 232 + 1;
  • 21 990 232 ÷ 2 = 10 995 116 + 0;
  • 10 995 116 ÷ 2 = 5 497 558 + 0;
  • 5 497 558 ÷ 2 = 2 748 779 + 0;
  • 2 748 779 ÷ 2 = 1 374 389 + 1;
  • 1 374 389 ÷ 2 = 687 194 + 1;
  • 687 194 ÷ 2 = 343 597 + 0;
  • 343 597 ÷ 2 = 171 798 + 1;
  • 171 798 ÷ 2 = 85 899 + 0;
  • 85 899 ÷ 2 = 42 949 + 1;
  • 42 949 ÷ 2 = 21 474 + 1;
  • 21 474 ÷ 2 = 10 737 + 0;
  • 10 737 ÷ 2 = 5 368 + 1;
  • 5 368 ÷ 2 = 2 684 + 0;
  • 2 684 ÷ 2 = 1 342 + 0;
  • 1 342 ÷ 2 = 671 + 0;
  • 671 ÷ 2 = 335 + 1;
  • 335 ÷ 2 = 167 + 1;
  • 167 ÷ 2 = 83 + 1;
  • 83 ÷ 2 = 41 + 1;
  • 41 ÷ 2 = 20 + 1;
  • 20 ÷ 2 = 10 + 0;
  • 10 ÷ 2 = 5 + 0;
  • 5 ÷ 2 = 2 + 1;
  • 2 ÷ 2 = 1 + 0;
  • 1 ÷ 2 = 0 + 1;

3. Construct the base 2 representation of the positive number:

Take all the remainders starting from the bottom of the list constructed above.


92 233 720 368 548(10) = 101 0011 1110 0010 1101 0110 0010 0011 1000 1101 1010 0100(2)


4. Determine the signed binary number bit length:

The base 2 number's actual length, in bits: 47.

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, 47,

3) so that the first bit (leftmost) could be zero
(we deal with a positive number at this moment)

=== is: 64.


5. 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.


92 233 720 368 548(10) = 0000 0000 0000 0000 0101 0011 1110 0010 1101 0110 0010 0011 1000 1101 1010 0100


6. Get the negative integer number representation. Part 1:

To write the negative integer number on 64 bits (8 Bytes),

as a signed binary in one's complement representation,

... replace all the bits on 0 with 1s and all the bits set on 1 with 0s.


Reverse the digits, flip the digits:

Replace the bits set on 0 with 1s and the bits set on 1 with 0s.

!(0000 0000 0000 0000 0101 0011 1110 0010 1101 0110 0010 0011 1000 1101 1010 0100)

= 1111 1111 1111 1111 1010 1100 0001 1101 0010 1001 1101 1100 0111 0010 0101 1011


7. Get the negative integer number representation. Part 2:

To write the negative integer number on 64 bits (8 Bytes),

as a signed binary in two's complement representation,

add 1 to the number calculated above

1111 1111 1111 1111 1010 1100 0001 1101 0010 1001 1101 1100 0111 0010 0101 1011

(to the signed binary in one's complement representation)


Binary addition carries on a value of 2:

0 + 0 = 0

0 + 1 = 1

1 + 1 = 10

1 + 10 = 11

1 + 11 = 100


Add 1 to the number calculated above
(to the signed binary number in one's complement representation):

-92 233 720 368 548 =

1111 1111 1111 1111 1010 1100 0001 1101 0010 1001 1101 1100 0111 0010 0101 1011 + 1


Number -92 233 720 368 548(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:

-92 233 720 368 548(10) = 1111 1111 1111 1111 1010 1100 0001 1101 0010 1001 1101 1100 0111 0010 0101 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 -92 233 720 368 549 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 -92 233 720 368 547 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