Two's Complement: Integer -> Binary: 111 110 000 100 008 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 111 110 000 100 008(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;
  • 111 110 000 100 008 ÷ 2 = 55 555 000 050 004 + 0;
  • 55 555 000 050 004 ÷ 2 = 27 777 500 025 002 + 0;
  • 27 777 500 025 002 ÷ 2 = 13 888 750 012 501 + 0;
  • 13 888 750 012 501 ÷ 2 = 6 944 375 006 250 + 1;
  • 6 944 375 006 250 ÷ 2 = 3 472 187 503 125 + 0;
  • 3 472 187 503 125 ÷ 2 = 1 736 093 751 562 + 1;
  • 1 736 093 751 562 ÷ 2 = 868 046 875 781 + 0;
  • 868 046 875 781 ÷ 2 = 434 023 437 890 + 1;
  • 434 023 437 890 ÷ 2 = 217 011 718 945 + 0;
  • 217 011 718 945 ÷ 2 = 108 505 859 472 + 1;
  • 108 505 859 472 ÷ 2 = 54 252 929 736 + 0;
  • 54 252 929 736 ÷ 2 = 27 126 464 868 + 0;
  • 27 126 464 868 ÷ 2 = 13 563 232 434 + 0;
  • 13 563 232 434 ÷ 2 = 6 781 616 217 + 0;
  • 6 781 616 217 ÷ 2 = 3 390 808 108 + 1;
  • 3 390 808 108 ÷ 2 = 1 695 404 054 + 0;
  • 1 695 404 054 ÷ 2 = 847 702 027 + 0;
  • 847 702 027 ÷ 2 = 423 851 013 + 1;
  • 423 851 013 ÷ 2 = 211 925 506 + 1;
  • 211 925 506 ÷ 2 = 105 962 753 + 0;
  • 105 962 753 ÷ 2 = 52 981 376 + 1;
  • 52 981 376 ÷ 2 = 26 490 688 + 0;
  • 26 490 688 ÷ 2 = 13 245 344 + 0;
  • 13 245 344 ÷ 2 = 6 622 672 + 0;
  • 6 622 672 ÷ 2 = 3 311 336 + 0;
  • 3 311 336 ÷ 2 = 1 655 668 + 0;
  • 1 655 668 ÷ 2 = 827 834 + 0;
  • 827 834 ÷ 2 = 413 917 + 0;
  • 413 917 ÷ 2 = 206 958 + 1;
  • 206 958 ÷ 2 = 103 479 + 0;
  • 103 479 ÷ 2 = 51 739 + 1;
  • 51 739 ÷ 2 = 25 869 + 1;
  • 25 869 ÷ 2 = 12 934 + 1;
  • 12 934 ÷ 2 = 6 467 + 0;
  • 6 467 ÷ 2 = 3 233 + 1;
  • 3 233 ÷ 2 = 1 616 + 1;
  • 1 616 ÷ 2 = 808 + 0;
  • 808 ÷ 2 = 404 + 0;
  • 404 ÷ 2 = 202 + 0;
  • 202 ÷ 2 = 101 + 0;
  • 101 ÷ 2 = 50 + 1;
  • 50 ÷ 2 = 25 + 0;
  • 25 ÷ 2 = 12 + 1;
  • 12 ÷ 2 = 6 + 0;
  • 6 ÷ 2 = 3 + 0;
  • 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.


111 110 000 100 008(10) = 110 0101 0000 1101 1101 0000 0001 0110 0100 0010 1010 1000(2)


3. 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.


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 111 110 000 100 008(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:

111 110 000 100 008(10) = 0000 0000 0000 0000 0110 0101 0000 1101 1101 0000 0001 0110 0100 0010 1010 1000

Spaces were used to group digits: for binary, by 4, for decimal, by 3.

Signed integer number 111 110 000 100 007 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 111 110 000 100 009 converted from decimal system (from base 10) and written as a signed binary in two's complement representation (written in base 2) = ?

Convert signed integer numbers from the decimal system (base ten) to signed binary in two's complement representation

How to convert a base 10 signed integer number to signed binary in two's complement representation:

1) Divide the positive version of number repeatedly by 2, keeping track of each remainder, till getting a quotient that is equal to 0.

2) Construct the base 2 representation by taking the previously calculated remainders starting from the last remainder up to the first one, in that order.

3) Construct the positive binary computer representation so that the first bit is 0.

4) Only if the initial number is negative, switch all the bits from 0 to 1 and from 1 to 0 (reversing the digits).

5) Only if the initial number is negative, add 1 to the number at the previous point.

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 111,110,000,100,008 from the decimal system (base 10) to a signed binary in two's complement representation Nov 28 10:11 UTC (GMT)
Convert and write the signed integer number 696,569,654,176 from the decimal system (base 10) to a signed binary in two's complement representation Nov 28 10:10 UTC (GMT)
Convert and write the signed integer number 10,100,075 from the decimal system (base 10) to a signed binary in two's complement representation Nov 28 10:10 UTC (GMT)
Convert and write the signed integer number 234,234,225 from the decimal system (base 10) to a signed binary in two's complement representation Nov 28 10:10 UTC (GMT)
Convert and write the signed integer number -52,708 from the decimal system (base 10) to a signed binary in two's complement representation Nov 28 10:10 UTC (GMT)
Convert and write the signed integer number -3,232,686 from the decimal system (base 10) to a signed binary in two's complement representation Nov 28 10:10 UTC (GMT)
Convert and write the signed integer number 2,815 from the decimal system (base 10) to a signed binary in two's complement representation Nov 28 10:09 UTC (GMT)
Convert and write the signed integer number 34,596 from the decimal system (base 10) to a signed binary in two's complement representation Nov 28 10:09 UTC (GMT)
Convert and write the signed integer number 237,650,367 from the decimal system (base 10) to a signed binary in two's complement representation Nov 28 10:09 UTC (GMT)
Convert and write the signed integer number -2,688 from the decimal system (base 10) to a signed binary in two's complement representation Nov 28 10:08 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