Convert 1 001 101 101 010 398 to a Signed Binary (Base 2)

How to convert 1 001 101 101 010 398(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 1 001 101 101 010 398 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;
  • 1 001 101 101 010 398 ÷ 2 = 500 550 550 505 199 + 0;
  • 500 550 550 505 199 ÷ 2 = 250 275 275 252 599 + 1;
  • 250 275 275 252 599 ÷ 2 = 125 137 637 626 299 + 1;
  • 125 137 637 626 299 ÷ 2 = 62 568 818 813 149 + 1;
  • 62 568 818 813 149 ÷ 2 = 31 284 409 406 574 + 1;
  • 31 284 409 406 574 ÷ 2 = 15 642 204 703 287 + 0;
  • 15 642 204 703 287 ÷ 2 = 7 821 102 351 643 + 1;
  • 7 821 102 351 643 ÷ 2 = 3 910 551 175 821 + 1;
  • 3 910 551 175 821 ÷ 2 = 1 955 275 587 910 + 1;
  • 1 955 275 587 910 ÷ 2 = 977 637 793 955 + 0;
  • 977 637 793 955 ÷ 2 = 488 818 896 977 + 1;
  • 488 818 896 977 ÷ 2 = 244 409 448 488 + 1;
  • 244 409 448 488 ÷ 2 = 122 204 724 244 + 0;
  • 122 204 724 244 ÷ 2 = 61 102 362 122 + 0;
  • 61 102 362 122 ÷ 2 = 30 551 181 061 + 0;
  • 30 551 181 061 ÷ 2 = 15 275 590 530 + 1;
  • 15 275 590 530 ÷ 2 = 7 637 795 265 + 0;
  • 7 637 795 265 ÷ 2 = 3 818 897 632 + 1;
  • 3 818 897 632 ÷ 2 = 1 909 448 816 + 0;
  • 1 909 448 816 ÷ 2 = 954 724 408 + 0;
  • 954 724 408 ÷ 2 = 477 362 204 + 0;
  • 477 362 204 ÷ 2 = 238 681 102 + 0;
  • 238 681 102 ÷ 2 = 119 340 551 + 0;
  • 119 340 551 ÷ 2 = 59 670 275 + 1;
  • 59 670 275 ÷ 2 = 29 835 137 + 1;
  • 29 835 137 ÷ 2 = 14 917 568 + 1;
  • 14 917 568 ÷ 2 = 7 458 784 + 0;
  • 7 458 784 ÷ 2 = 3 729 392 + 0;
  • 3 729 392 ÷ 2 = 1 864 696 + 0;
  • 1 864 696 ÷ 2 = 932 348 + 0;
  • 932 348 ÷ 2 = 466 174 + 0;
  • 466 174 ÷ 2 = 233 087 + 0;
  • 233 087 ÷ 2 = 116 543 + 1;
  • 116 543 ÷ 2 = 58 271 + 1;
  • 58 271 ÷ 2 = 29 135 + 1;
  • 29 135 ÷ 2 = 14 567 + 1;
  • 14 567 ÷ 2 = 7 283 + 1;
  • 7 283 ÷ 2 = 3 641 + 1;
  • 3 641 ÷ 2 = 1 820 + 1;
  • 1 820 ÷ 2 = 910 + 0;
  • 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.

1 001 101 101 010 398(10) = 11 1000 1110 0111 1111 0000 0011 1000 0010 1000 1101 1101 1110(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:


1 001 101 101 010 398(10) Base 10 integer number converted and written as a signed binary code (in base 2):

1 001 101 101 010 398(10) = 0000 0000 0000 0011 1000 1110 0111 1111 0000 0011 1000 0010 1000 1101 1101 1110

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