Integer to Signed Binary: Number 279 274 843 Converted and Written as a Signed Binary. Base Ten Decimal System Conversion

Integer number 279 274 843(10) written as a signed binary number

How to convert the base ten signed integer number 279 274 843 to base two:

  • A signed integer, written in base ten, or a decimal system number, is a number written using the digits 0 through 9 and the sign, which can be positive (+) or negative (-). If positive, the sign is usually not written. A number written in base two, or binary, is a number written using only the digits 0 and 1.

  • To convert a base ten signed number (written as an integer in decimal system) to base two, written as a signed binary, follow the steps below.

  • Divide the number repeatedly by 2: keep track of each remainder.
  • Stop when you get a quotient that is equal to zero.
  • Construct the base 2 representation of the positive number: take all the remainders starting from the bottom of the list constructed above.
  • Determine the signed binary number bit length.
  • Get the binary computer representation: if needed, add extra 0s in front (to the left) of the base 2 number, up to the required length and change the first bit (the leftmost), from 0 to 1, if the number is negative.
  • Below you can see the conversion process to a signed binary and the related calculations.

1. Divide the number repeatedly by 2:

Keep track of each remainder.

Stop when you get a quotient that is equal to zero.


  • division = quotient + remainder;
  • 279 274 843 ÷ 2 = 139 637 421 + 1;
  • 139 637 421 ÷ 2 = 69 818 710 + 1;
  • 69 818 710 ÷ 2 = 34 909 355 + 0;
  • 34 909 355 ÷ 2 = 17 454 677 + 1;
  • 17 454 677 ÷ 2 = 8 727 338 + 1;
  • 8 727 338 ÷ 2 = 4 363 669 + 0;
  • 4 363 669 ÷ 2 = 2 181 834 + 1;
  • 2 181 834 ÷ 2 = 1 090 917 + 0;
  • 1 090 917 ÷ 2 = 545 458 + 1;
  • 545 458 ÷ 2 = 272 729 + 0;
  • 272 729 ÷ 2 = 136 364 + 1;
  • 136 364 ÷ 2 = 68 182 + 0;
  • 68 182 ÷ 2 = 34 091 + 0;
  • 34 091 ÷ 2 = 17 045 + 1;
  • 17 045 ÷ 2 = 8 522 + 1;
  • 8 522 ÷ 2 = 4 261 + 0;
  • 4 261 ÷ 2 = 2 130 + 1;
  • 2 130 ÷ 2 = 1 065 + 0;
  • 1 065 ÷ 2 = 532 + 1;
  • 532 ÷ 2 = 266 + 0;
  • 266 ÷ 2 = 133 + 0;
  • 133 ÷ 2 = 66 + 1;
  • 66 ÷ 2 = 33 + 0;
  • 33 ÷ 2 = 16 + 1;
  • 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.

279 274 843(10) = 1 0000 1010 0101 0110 0101 0101 1011(2)


3. Determine the signed binary number bit length:

  • The base 2 number's actual length, in bits: 29.

  • 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, 29,

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

=== is: 32.


4. Get the positive binary computer representation on 32 bits (4 Bytes):

If needed, add extra 0s in front (to the left) of the base 2 number, up to the required length, 32:


Number 279 274 843(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):

279 274 843(10) = 0001 0000 1010 0101 0110 0101 0101 1011

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

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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