Two's Complement: Integer ↗ Binary: 47 245 689 088 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 47 245 689 088(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;
  • 47 245 689 088 ÷ 2 = 23 622 844 544 + 0;
  • 23 622 844 544 ÷ 2 = 11 811 422 272 + 0;
  • 11 811 422 272 ÷ 2 = 5 905 711 136 + 0;
  • 5 905 711 136 ÷ 2 = 2 952 855 568 + 0;
  • 2 952 855 568 ÷ 2 = 1 476 427 784 + 0;
  • 1 476 427 784 ÷ 2 = 738 213 892 + 0;
  • 738 213 892 ÷ 2 = 369 106 946 + 0;
  • 369 106 946 ÷ 2 = 184 553 473 + 0;
  • 184 553 473 ÷ 2 = 92 276 736 + 1;
  • 92 276 736 ÷ 2 = 46 138 368 + 0;
  • 46 138 368 ÷ 2 = 23 069 184 + 0;
  • 23 069 184 ÷ 2 = 11 534 592 + 0;
  • 11 534 592 ÷ 2 = 5 767 296 + 0;
  • 5 767 296 ÷ 2 = 2 883 648 + 0;
  • 2 883 648 ÷ 2 = 1 441 824 + 0;
  • 1 441 824 ÷ 2 = 720 912 + 0;
  • 720 912 ÷ 2 = 360 456 + 0;
  • 360 456 ÷ 2 = 180 228 + 0;
  • 180 228 ÷ 2 = 90 114 + 0;
  • 90 114 ÷ 2 = 45 057 + 0;
  • 45 057 ÷ 2 = 22 528 + 1;
  • 22 528 ÷ 2 = 11 264 + 0;
  • 11 264 ÷ 2 = 5 632 + 0;
  • 5 632 ÷ 2 = 2 816 + 0;
  • 2 816 ÷ 2 = 1 408 + 0;
  • 1 408 ÷ 2 = 704 + 0;
  • 704 ÷ 2 = 352 + 0;
  • 352 ÷ 2 = 176 + 0;
  • 176 ÷ 2 = 88 + 0;
  • 88 ÷ 2 = 44 + 0;
  • 44 ÷ 2 = 22 + 0;
  • 22 ÷ 2 = 11 + 0;
  • 11 ÷ 2 = 5 + 1;
  • 5 ÷ 2 = 2 + 1;
  • 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.


47 245 689 088(10) = 1011 0000 0000 0001 0000 0000 0001 0000 0000(2)


3. Determine the signed binary number bit length:

The base 2 number's actual length, in bits: 36.

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, 36,

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 47 245 689 088(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:

47 245 689 088(10) = 0000 0000 0000 0000 0000 0000 0000 1011 0000 0000 0001 0000 0000 0001 0000 0000

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 47 245 689 087 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 47 245 689 089 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 381,497,542 from the decimal system (base 10) to a signed binary in two's complement representation Apr 18 00:30 UTC (GMT)
Convert and write the signed integer number 1,964 from the decimal system (base 10) to a signed binary in two's complement representation Apr 18 00:30 UTC (GMT)
Convert and write the signed integer number 134,217,669 from the decimal system (base 10) to a signed binary in two's complement representation Apr 18 00:30 UTC (GMT)
Convert and write the signed integer number 1,456,777,255,814,994 from the decimal system (base 10) to a signed binary in two's complement representation Apr 18 00:30 UTC (GMT)
Convert and write the signed integer number 13 from the decimal system (base 10) to a signed binary in two's complement representation Apr 18 00:29 UTC (GMT)
Convert and write the signed integer number -46 from the decimal system (base 10) to a signed binary in two's complement representation Apr 18 00:29 UTC (GMT)
Convert and write the signed integer number 7,734,520 from the decimal system (base 10) to a signed binary in two's complement representation Apr 18 00:29 UTC (GMT)
Convert and write the signed integer number -3,733 from the decimal system (base 10) to a signed binary in two's complement representation Apr 18 00:29 UTC (GMT)
Convert and write the signed integer number 34 from the decimal system (base 10) to a signed binary in two's complement representation Apr 18 00:29 UTC (GMT)
Convert and write the signed integer number 1,100,111,100,009,934 from the decimal system (base 10) to a signed binary in two's complement representation Apr 18 00:29 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