Integer to Signed Binary: Number 1 000 110 374 Converted and Written as a Signed Binary. Base Ten Decimal System Conversion

Integer number 1 000 110 374(10) written as a signed binary number

How to convert the base ten signed integer number 1 000 110 374 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;
  • 1 000 110 374 ÷ 2 = 500 055 187 + 0;
  • 500 055 187 ÷ 2 = 250 027 593 + 1;
  • 250 027 593 ÷ 2 = 125 013 796 + 1;
  • 125 013 796 ÷ 2 = 62 506 898 + 0;
  • 62 506 898 ÷ 2 = 31 253 449 + 0;
  • 31 253 449 ÷ 2 = 15 626 724 + 1;
  • 15 626 724 ÷ 2 = 7 813 362 + 0;
  • 7 813 362 ÷ 2 = 3 906 681 + 0;
  • 3 906 681 ÷ 2 = 1 953 340 + 1;
  • 1 953 340 ÷ 2 = 976 670 + 0;
  • 976 670 ÷ 2 = 488 335 + 0;
  • 488 335 ÷ 2 = 244 167 + 1;
  • 244 167 ÷ 2 = 122 083 + 1;
  • 122 083 ÷ 2 = 61 041 + 1;
  • 61 041 ÷ 2 = 30 520 + 1;
  • 30 520 ÷ 2 = 15 260 + 0;
  • 15 260 ÷ 2 = 7 630 + 0;
  • 7 630 ÷ 2 = 3 815 + 0;
  • 3 815 ÷ 2 = 1 907 + 1;
  • 1 907 ÷ 2 = 953 + 1;
  • 953 ÷ 2 = 476 + 1;
  • 476 ÷ 2 = 238 + 0;
  • 238 ÷ 2 = 119 + 0;
  • 119 ÷ 2 = 59 + 1;
  • 59 ÷ 2 = 29 + 1;
  • 29 ÷ 2 = 14 + 1;
  • 14 ÷ 2 = 7 + 0;
  • 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.

1 000 110 374(10) = 11 1011 1001 1100 0111 1001 0010 0110(2)


3. Determine the signed binary number bit length:

  • The base 2 number's actual length, in bits: 30.

  • 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, 30,

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 1 000 110 374(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):

1 000 110 374(10) = 0011 1011 1001 1100 0111 1001 0010 0110

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