Convert 1 111 000 010 000 470 to a Signed Binary (Base 2)

How to convert 1 111 000 010 000 470(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 1 111 000 010 000 470 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;
  • 1 111 000 010 000 470 ÷ 2 = 555 500 005 000 235 + 0;
  • 555 500 005 000 235 ÷ 2 = 277 750 002 500 117 + 1;
  • 277 750 002 500 117 ÷ 2 = 138 875 001 250 058 + 1;
  • 138 875 001 250 058 ÷ 2 = 69 437 500 625 029 + 0;
  • 69 437 500 625 029 ÷ 2 = 34 718 750 312 514 + 1;
  • 34 718 750 312 514 ÷ 2 = 17 359 375 156 257 + 0;
  • 17 359 375 156 257 ÷ 2 = 8 679 687 578 128 + 1;
  • 8 679 687 578 128 ÷ 2 = 4 339 843 789 064 + 0;
  • 4 339 843 789 064 ÷ 2 = 2 169 921 894 532 + 0;
  • 2 169 921 894 532 ÷ 2 = 1 084 960 947 266 + 0;
  • 1 084 960 947 266 ÷ 2 = 542 480 473 633 + 0;
  • 542 480 473 633 ÷ 2 = 271 240 236 816 + 1;
  • 271 240 236 816 ÷ 2 = 135 620 118 408 + 0;
  • 135 620 118 408 ÷ 2 = 67 810 059 204 + 0;
  • 67 810 059 204 ÷ 2 = 33 905 029 602 + 0;
  • 33 905 029 602 ÷ 2 = 16 952 514 801 + 0;
  • 16 952 514 801 ÷ 2 = 8 476 257 400 + 1;
  • 8 476 257 400 ÷ 2 = 4 238 128 700 + 0;
  • 4 238 128 700 ÷ 2 = 2 119 064 350 + 0;
  • 2 119 064 350 ÷ 2 = 1 059 532 175 + 0;
  • 1 059 532 175 ÷ 2 = 529 766 087 + 1;
  • 529 766 087 ÷ 2 = 264 883 043 + 1;
  • 264 883 043 ÷ 2 = 132 441 521 + 1;
  • 132 441 521 ÷ 2 = 66 220 760 + 1;
  • 66 220 760 ÷ 2 = 33 110 380 + 0;
  • 33 110 380 ÷ 2 = 16 555 190 + 0;
  • 16 555 190 ÷ 2 = 8 277 595 + 0;
  • 8 277 595 ÷ 2 = 4 138 797 + 1;
  • 4 138 797 ÷ 2 = 2 069 398 + 1;
  • 2 069 398 ÷ 2 = 1 034 699 + 0;
  • 1 034 699 ÷ 2 = 517 349 + 1;
  • 517 349 ÷ 2 = 258 674 + 1;
  • 258 674 ÷ 2 = 129 337 + 0;
  • 129 337 ÷ 2 = 64 668 + 1;
  • 64 668 ÷ 2 = 32 334 + 0;
  • 32 334 ÷ 2 = 16 167 + 0;
  • 16 167 ÷ 2 = 8 083 + 1;
  • 8 083 ÷ 2 = 4 041 + 1;
  • 4 041 ÷ 2 = 2 020 + 1;
  • 2 020 ÷ 2 = 1 010 + 0;
  • 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.

1 111 000 010 000 470(10) = 11 1111 0010 0111 0010 1101 1000 1111 0001 0000 1000 0101 0110(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:


1 111 000 010 000 470(10) Base 10 integer number converted and written as a signed binary code (in base 2):

1 111 000 010 000 470(10) = 0000 0000 0000 0011 1111 0010 0111 0010 1101 1000 1111 0001 0000 1000 0101 0110

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

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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