Convert 1 001 110 010 000 043 to a Signed Binary (Base 2)

How to convert 1 001 110 010 000 043(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 1 001 110 010 000 043 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;
  • 1 001 110 010 000 043 ÷ 2 = 500 555 005 000 021 + 1;
  • 500 555 005 000 021 ÷ 2 = 250 277 502 500 010 + 1;
  • 250 277 502 500 010 ÷ 2 = 125 138 751 250 005 + 0;
  • 125 138 751 250 005 ÷ 2 = 62 569 375 625 002 + 1;
  • 62 569 375 625 002 ÷ 2 = 31 284 687 812 501 + 0;
  • 31 284 687 812 501 ÷ 2 = 15 642 343 906 250 + 1;
  • 15 642 343 906 250 ÷ 2 = 7 821 171 953 125 + 0;
  • 7 821 171 953 125 ÷ 2 = 3 910 585 976 562 + 1;
  • 3 910 585 976 562 ÷ 2 = 1 955 292 988 281 + 0;
  • 1 955 292 988 281 ÷ 2 = 977 646 494 140 + 1;
  • 977 646 494 140 ÷ 2 = 488 823 247 070 + 0;
  • 488 823 247 070 ÷ 2 = 244 411 623 535 + 0;
  • 244 411 623 535 ÷ 2 = 122 205 811 767 + 1;
  • 122 205 811 767 ÷ 2 = 61 102 905 883 + 1;
  • 61 102 905 883 ÷ 2 = 30 551 452 941 + 1;
  • 30 551 452 941 ÷ 2 = 15 275 726 470 + 1;
  • 15 275 726 470 ÷ 2 = 7 637 863 235 + 0;
  • 7 637 863 235 ÷ 2 = 3 818 931 617 + 1;
  • 3 818 931 617 ÷ 2 = 1 909 465 808 + 1;
  • 1 909 465 808 ÷ 2 = 954 732 904 + 0;
  • 954 732 904 ÷ 2 = 477 366 452 + 0;
  • 477 366 452 ÷ 2 = 238 683 226 + 0;
  • 238 683 226 ÷ 2 = 119 341 613 + 0;
  • 119 341 613 ÷ 2 = 59 670 806 + 1;
  • 59 670 806 ÷ 2 = 29 835 403 + 0;
  • 29 835 403 ÷ 2 = 14 917 701 + 1;
  • 14 917 701 ÷ 2 = 7 458 850 + 1;
  • 7 458 850 ÷ 2 = 3 729 425 + 0;
  • 3 729 425 ÷ 2 = 1 864 712 + 1;
  • 1 864 712 ÷ 2 = 932 356 + 0;
  • 932 356 ÷ 2 = 466 178 + 0;
  • 466 178 ÷ 2 = 233 089 + 0;
  • 233 089 ÷ 2 = 116 544 + 1;
  • 116 544 ÷ 2 = 58 272 + 0;
  • 58 272 ÷ 2 = 29 136 + 0;
  • 29 136 ÷ 2 = 14 568 + 0;
  • 14 568 ÷ 2 = 7 284 + 0;
  • 7 284 ÷ 2 = 3 642 + 0;
  • 3 642 ÷ 2 = 1 821 + 0;
  • 1 821 ÷ 2 = 910 + 1;
  • 910 ÷ 2 = 455 + 0;
  • 455 ÷ 2 = 227 + 1;
  • 227 ÷ 2 = 113 + 1;
  • 113 ÷ 2 = 56 + 1;
  • 56 ÷ 2 = 28 + 0;
  • 28 ÷ 2 = 14 + 0;
  • 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.

1 001 110 010 000 043(10) = 11 1000 1110 1000 0001 0001 0110 1000 0110 1111 0010 1010 1011(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:


1 001 110 010 000 043(10) Base 10 integer number converted and written as a signed binary code (in base 2):

1 001 110 010 000 043(10) = 0000 0000 0000 0011 1000 1110 1000 0001 0001 0110 1000 0110 1111 0010 1010 1011

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