Signed Binary: Integer Number 4 324 020 245 Converted and Written as a Signed Binary. Base Ten Decimal System Numbers Conversions

Integer number 4 324 020 245(10) written as a signed binary number

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;
  • 4 324 020 245 ÷ 2 = 2 162 010 122 + 1;
  • 2 162 010 122 ÷ 2 = 1 081 005 061 + 0;
  • 1 081 005 061 ÷ 2 = 540 502 530 + 1;
  • 540 502 530 ÷ 2 = 270 251 265 + 0;
  • 270 251 265 ÷ 2 = 135 125 632 + 1;
  • 135 125 632 ÷ 2 = 67 562 816 + 0;
  • 67 562 816 ÷ 2 = 33 781 408 + 0;
  • 33 781 408 ÷ 2 = 16 890 704 + 0;
  • 16 890 704 ÷ 2 = 8 445 352 + 0;
  • 8 445 352 ÷ 2 = 4 222 676 + 0;
  • 4 222 676 ÷ 2 = 2 111 338 + 0;
  • 2 111 338 ÷ 2 = 1 055 669 + 0;
  • 1 055 669 ÷ 2 = 527 834 + 1;
  • 527 834 ÷ 2 = 263 917 + 0;
  • 263 917 ÷ 2 = 131 958 + 1;
  • 131 958 ÷ 2 = 65 979 + 0;
  • 65 979 ÷ 2 = 32 989 + 1;
  • 32 989 ÷ 2 = 16 494 + 1;
  • 16 494 ÷ 2 = 8 247 + 0;
  • 8 247 ÷ 2 = 4 123 + 1;
  • 4 123 ÷ 2 = 2 061 + 1;
  • 2 061 ÷ 2 = 1 030 + 1;
  • 1 030 ÷ 2 = 515 + 0;
  • 515 ÷ 2 = 257 + 1;
  • 257 ÷ 2 = 128 + 1;
  • 128 ÷ 2 = 64 + 0;
  • 64 ÷ 2 = 32 + 0;
  • 32 ÷ 2 = 16 + 0;
  • 16 ÷ 2 = 8 + 0;
  • 8 ÷ 2 = 4 + 0;
  • 4 ÷ 2 = 2 + 0;
  • 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.


4 324 020 245(10) = 1 0000 0001 1011 1011 0101 0000 0001 0101(2)


3. Determine the signed binary number bit length:

The base 2 number's actual length, in bits: 33.

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) is reserved for 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, 33,

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 4 324 020 245(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):

4 324 020 245(10) = 0000 0000 0000 0000 0000 0000 0000 0001 0000 0001 1011 1011 0101 0000 0001 0101

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

» Integer number 4 324 020 216 converted and written as a signed binary number

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How to convert signed integers from decimal system to binary code system

Follow the steps below to convert a signed base ten integer number to signed binary:

  • 1. In a signed binary, first bit (the leftmost) is reserved for sign: 0 = positive integer number, 1 = positive integer number. If the number to be converted is negative, start with its positive version.
  • 2. Divide repeatedly by 2 the positive integer number keeping track of each remainder. STOP when 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 have a length of 4, 8, 16, 32, 64, ... bits (power of 2) - if needed, fill in extra '0' bits in front of the base 2 number (to the left), up to the right length; this way the first bit (the leftmost one) is always '0', as for a positive representation.
  • 5. To get the negative reprezentation of the number, simply switch the first bit (the leftmost one), from '0' to '1'.

Example: convert the negative number -63 from decimal system (base ten) to signed binary code system:

  • 1. Start with the positive version of the number: |-63| = 63;
  • 2. Divide repeatedly 63 by 2, keeping track of each remainder, until we get a quotient that is equal to zero:
    • division = quotient + remainder
    • 63 ÷ 2 = 31 + 1
    • 31 ÷ 2 = 15 + 1
    • 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:
    63(10) = 11 1111(2)
  • 4. The actual length of base 2 representation number is 6, so the positive binary computer representation length of the signed binary will take in this case 8 bits (the least power of 2 higher than 6) - add extra '0's in front (to the left), up to the required length; this way the first bit (the leftmost one) is to be '0', as for a positive number:
    63(10) = 0011 1111(2)
  • 5. To get the negative integer number representation simply change the first bit (the leftmost), from '0' to '1':
    -63(10) = 1011 1111
  • Number -63(10), signed integer, converted from decimal system (base 10) to signed binary = 1011 1111