Two's Complement: Integer ↗ Binary: 1 111 111 011 101 163 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 1 111 111 011 101 163(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;
  • 1 111 111 011 101 163 ÷ 2 = 555 555 505 550 581 + 1;
  • 555 555 505 550 581 ÷ 2 = 277 777 752 775 290 + 1;
  • 277 777 752 775 290 ÷ 2 = 138 888 876 387 645 + 0;
  • 138 888 876 387 645 ÷ 2 = 69 444 438 193 822 + 1;
  • 69 444 438 193 822 ÷ 2 = 34 722 219 096 911 + 0;
  • 34 722 219 096 911 ÷ 2 = 17 361 109 548 455 + 1;
  • 17 361 109 548 455 ÷ 2 = 8 680 554 774 227 + 1;
  • 8 680 554 774 227 ÷ 2 = 4 340 277 387 113 + 1;
  • 4 340 277 387 113 ÷ 2 = 2 170 138 693 556 + 1;
  • 2 170 138 693 556 ÷ 2 = 1 085 069 346 778 + 0;
  • 1 085 069 346 778 ÷ 2 = 542 534 673 389 + 0;
  • 542 534 673 389 ÷ 2 = 271 267 336 694 + 1;
  • 271 267 336 694 ÷ 2 = 135 633 668 347 + 0;
  • 135 633 668 347 ÷ 2 = 67 816 834 173 + 1;
  • 67 816 834 173 ÷ 2 = 33 908 417 086 + 1;
  • 33 908 417 086 ÷ 2 = 16 954 208 543 + 0;
  • 16 954 208 543 ÷ 2 = 8 477 104 271 + 1;
  • 8 477 104 271 ÷ 2 = 4 238 552 135 + 1;
  • 4 238 552 135 ÷ 2 = 2 119 276 067 + 1;
  • 2 119 276 067 ÷ 2 = 1 059 638 033 + 1;
  • 1 059 638 033 ÷ 2 = 529 819 016 + 1;
  • 529 819 016 ÷ 2 = 264 909 508 + 0;
  • 264 909 508 ÷ 2 = 132 454 754 + 0;
  • 132 454 754 ÷ 2 = 66 227 377 + 0;
  • 66 227 377 ÷ 2 = 33 113 688 + 1;
  • 33 113 688 ÷ 2 = 16 556 844 + 0;
  • 16 556 844 ÷ 2 = 8 278 422 + 0;
  • 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.


1 111 111 011 101 163(10) = 11 1111 0010 1000 1100 1011 0001 0001 1111 0110 1001 1110 1011(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 1 111 111 011 101 163(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:

1 111 111 011 101 163(10) = 0000 0000 0000 0011 1111 0010 1000 1100 1011 0001 0001 1111 0110 1001 1110 1011

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 1 111 111 011 101 162 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 1 111 111 011 101 164 converted from decimal system (from base 10) and written as a signed binary in two's complement representation (written in base 2) = ?

The latest signed integer numbers written in base ten converted from decimal system to binary two's complement representation

Convert and write the signed integer number 100,100,110,927 from the decimal system (base 10) to a signed binary in two's complement representation May 01 11:06 UTC (GMT)
Convert and write the signed integer number 95,902 from the decimal system (base 10) to a signed binary in two's complement representation May 01 11:06 UTC (GMT)
Convert and write the signed integer number 101,111,010,152 from the decimal system (base 10) to a signed binary in two's complement representation May 01 11:06 UTC (GMT)
Convert and write the signed integer number -126 from the decimal system (base 10) to a signed binary in two's complement representation May 01 11:05 UTC (GMT)
Convert and write the signed integer number -24,163 from the decimal system (base 10) to a signed binary in two's complement representation May 01 11:05 UTC (GMT)
Convert and write the signed integer number 7,260,028 from the decimal system (base 10) to a signed binary in two's complement representation May 01 11:05 UTC (GMT)
Convert and write the signed integer number 1,100,110,010,109,883 from the decimal system (base 10) to a signed binary in two's complement representation May 01 11:05 UTC (GMT)
Convert and write the signed integer number 100,101,010,111 from the decimal system (base 10) to a signed binary in two's complement representation May 01 11:05 UTC (GMT)
Convert and write the signed integer number 864,519 from the decimal system (base 10) to a signed binary in two's complement representation May 01 11:05 UTC (GMT)
Convert and write the signed integer number 23,923 from the decimal system (base 10) to a signed binary in two's complement representation May 01 11:04 UTC (GMT)
All the decimal system integer numbers converted and written as signed binary numbers in two's complement representation

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