Convert 1 111 111 111 010 224, Signed Base 10 Integer Number, Write It as Signed Binary Code (Base 2) Equivalent

How to convert 1 111 111 111 010 224(10), a signed base 10 integer number? How to write it as a signed binary code in base 2

What are the required steps to convert base 10 integer
number 1 111 111 111 010 224 to signed binary code (in base 2)?

  • 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.

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;
  • 1 111 111 111 010 224 ÷ 2 = 555 555 555 505 112 + 0;
  • 555 555 555 505 112 ÷ 2 = 277 777 777 752 556 + 0;
  • 277 777 777 752 556 ÷ 2 = 138 888 888 876 278 + 0;
  • 138 888 888 876 278 ÷ 2 = 69 444 444 438 139 + 0;
  • 69 444 444 438 139 ÷ 2 = 34 722 222 219 069 + 1;
  • 34 722 222 219 069 ÷ 2 = 17 361 111 109 534 + 1;
  • 17 361 111 109 534 ÷ 2 = 8 680 555 554 767 + 0;
  • 8 680 555 554 767 ÷ 2 = 4 340 277 777 383 + 1;
  • 4 340 277 777 383 ÷ 2 = 2 170 138 888 691 + 1;
  • 2 170 138 888 691 ÷ 2 = 1 085 069 444 345 + 1;
  • 1 085 069 444 345 ÷ 2 = 542 534 722 172 + 1;
  • 542 534 722 172 ÷ 2 = 271 267 361 086 + 0;
  • 271 267 361 086 ÷ 2 = 135 633 680 543 + 0;
  • 135 633 680 543 ÷ 2 = 67 816 840 271 + 1;
  • 67 816 840 271 ÷ 2 = 33 908 420 135 + 1;
  • 33 908 420 135 ÷ 2 = 16 954 210 067 + 1;
  • 16 954 210 067 ÷ 2 = 8 477 105 033 + 1;
  • 8 477 105 033 ÷ 2 = 4 238 552 516 + 1;
  • 4 238 552 516 ÷ 2 = 2 119 276 258 + 0;
  • 2 119 276 258 ÷ 2 = 1 059 638 129 + 0;
  • 1 059 638 129 ÷ 2 = 529 819 064 + 1;
  • 529 819 064 ÷ 2 = 264 909 532 + 0;
  • 264 909 532 ÷ 2 = 132 454 766 + 0;
  • 132 454 766 ÷ 2 = 66 227 383 + 0;
  • 66 227 383 ÷ 2 = 33 113 691 + 1;
  • 33 113 691 ÷ 2 = 16 556 845 + 1;
  • 16 556 845 ÷ 2 = 8 278 422 + 1;
  • 8 278 422 ÷ 2 = 4 139 211 + 0;
  • 4 139 211 ÷ 2 = 2 069 605 + 1;
  • 2 069 605 ÷ 2 = 1 034 802 + 1;
  • 1 034 802 ÷ 2 = 517 401 + 0;
  • 517 401 ÷ 2 = 258 700 + 1;
  • 258 700 ÷ 2 = 129 350 + 0;
  • 129 350 ÷ 2 = 64 675 + 0;
  • 64 675 ÷ 2 = 32 337 + 1;
  • 32 337 ÷ 2 = 16 168 + 1;
  • 16 168 ÷ 2 = 8 084 + 0;
  • 8 084 ÷ 2 = 4 042 + 0;
  • 4 042 ÷ 2 = 2 021 + 0;
  • 2 021 ÷ 2 = 1 010 + 1;
  • 1 010 ÷ 2 = 505 + 0;
  • 505 ÷ 2 = 252 + 1;
  • 252 ÷ 2 = 126 + 0;
  • 126 ÷ 2 = 63 + 0;
  • 63 ÷ 2 = 31 + 1;
  • 31 ÷ 2 = 15 + 1;
  • 15 ÷ 2 = 7 + 1;
  • 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.

1 111 111 111 010 224(10) = 11 1111 0010 1000 1100 1011 0111 0001 0011 1110 0111 1011 0000(2)


3. Determine the signed binary number bit length:

  • The base 2 number's actual length, in bits: 50.

  • 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, 50,

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:


1 111 111 111 010 224(10) Base 10 integer number converted and written as a signed binary code (in base 2):

1 111 111 111 010 224(10) = 0000 0000 0000 0011 1111 0010 1000 1100 1011 0111 0001 0011 1110 0111 1011 0000

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

Share

» More ops: Convert 1 111 111 111 010 247, a signed base 10 integer number, write it as a signed binary code (in base 2) equivalent

» Calculations Performed by Our Visitors: Signed base 10 integer numbers converted and written as signed binary code (base 2) equivalents. Data organized on a Monthly Basis

» Month 05, 2025 [May]: Signed base 10 integer numbers converted and written as signed binary code. Calculations performed during the month of: May - by our visitors

How to convert signed base 10 integers in decimal 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