Base ten decimal system signed integer number 2 753 069 380 527 989 converted to signed binary

How to convert the signed integer in decimal system (in base 10):
2 753 069 380 527 989(10)
to a signed binary

1. Divide the number repeatedly by 2, keeping track of each remainder, until we get a quotient that is equal to zero:

  • division = quotient + remainder;
  • 2 753 069 380 527 989 ÷ 2 = 1 376 534 690 263 994 + 1;
  • 1 376 534 690 263 994 ÷ 2 = 688 267 345 131 997 + 0;
  • 688 267 345 131 997 ÷ 2 = 344 133 672 565 998 + 1;
  • 344 133 672 565 998 ÷ 2 = 172 066 836 282 999 + 0;
  • 172 066 836 282 999 ÷ 2 = 86 033 418 141 499 + 1;
  • 86 033 418 141 499 ÷ 2 = 43 016 709 070 749 + 1;
  • 43 016 709 070 749 ÷ 2 = 21 508 354 535 374 + 1;
  • 21 508 354 535 374 ÷ 2 = 10 754 177 267 687 + 0;
  • 10 754 177 267 687 ÷ 2 = 5 377 088 633 843 + 1;
  • 5 377 088 633 843 ÷ 2 = 2 688 544 316 921 + 1;
  • 2 688 544 316 921 ÷ 2 = 1 344 272 158 460 + 1;
  • 1 344 272 158 460 ÷ 2 = 672 136 079 230 + 0;
  • 672 136 079 230 ÷ 2 = 336 068 039 615 + 0;
  • 336 068 039 615 ÷ 2 = 168 034 019 807 + 1;
  • 168 034 019 807 ÷ 2 = 84 017 009 903 + 1;
  • 84 017 009 903 ÷ 2 = 42 008 504 951 + 1;
  • 42 008 504 951 ÷ 2 = 21 004 252 475 + 1;
  • 21 004 252 475 ÷ 2 = 10 502 126 237 + 1;
  • 10 502 126 237 ÷ 2 = 5 251 063 118 + 1;
  • 5 251 063 118 ÷ 2 = 2 625 531 559 + 0;
  • 2 625 531 559 ÷ 2 = 1 312 765 779 + 1;
  • 1 312 765 779 ÷ 2 = 656 382 889 + 1;
  • 656 382 889 ÷ 2 = 328 191 444 + 1;
  • 328 191 444 ÷ 2 = 164 095 722 + 0;
  • 164 095 722 ÷ 2 = 82 047 861 + 0;
  • 82 047 861 ÷ 2 = 41 023 930 + 1;
  • 41 023 930 ÷ 2 = 20 511 965 + 0;
  • 20 511 965 ÷ 2 = 10 255 982 + 1;
  • 10 255 982 ÷ 2 = 5 127 991 + 0;
  • 5 127 991 ÷ 2 = 2 563 995 + 1;
  • 2 563 995 ÷ 2 = 1 281 997 + 1;
  • 1 281 997 ÷ 2 = 640 998 + 1;
  • 640 998 ÷ 2 = 320 499 + 0;
  • 320 499 ÷ 2 = 160 249 + 1;
  • 160 249 ÷ 2 = 80 124 + 1;
  • 80 124 ÷ 2 = 40 062 + 0;
  • 40 062 ÷ 2 = 20 031 + 0;
  • 20 031 ÷ 2 = 10 015 + 1;
  • 10 015 ÷ 2 = 5 007 + 1;
  • 5 007 ÷ 2 = 2 503 + 1;
  • 2 503 ÷ 2 = 1 251 + 1;
  • 1 251 ÷ 2 = 625 + 1;
  • 625 ÷ 2 = 312 + 1;
  • 312 ÷ 2 = 156 + 0;
  • 156 ÷ 2 = 78 + 0;
  • 78 ÷ 2 = 39 + 0;
  • 39 ÷ 2 = 19 + 1;
  • 19 ÷ 2 = 9 + 1;
  • 9 ÷ 2 = 4 + 1;
  • 4 ÷ 2 = 2 + 0;
  • 2 ÷ 2 = 1 + 0;
  • 1 ÷ 2 = 0 + 1;

2. Construct the base 2 representation of the positive number, by taking all the remainders starting from the bottom of the list constructed above:

2 753 069 380 527 989(10) = 1001 1100 0111 1110 0110 1110 1010 0111 0111 1110 0111 0111 0101(2)

3. Determine the signed binary number bit length:

The base 2 number's actual length, in bits: 52.

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; ...

First bit (the leftmost) is reserved for the sign:
0 = positive integer number, 1 = negative integer number

The least number that is a power of 2 and is larger than the actual length so that the first bit (leftmost) could be zero is: 64.

4. 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:

2 753 069 380 527 989(10) = 0000 0000 0000 1001 1100 0111 1110 0110 1110 1010 0111 0111 1110 0111 0111 0101

Conclusion:

Number 2 753 069 380 527 989, a signed integer, converted from decimal system (base 10) to signed binary:
2 753 069 380 527 989(10) = 0000 0000 0000 1001 1100 0111 1110 0110 1110 1010 0111 0111 1110 0111 0111 0101

First bit (the leftmost) is reserved for the sign:
0 = positive integer number, 1 = negative integer number


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

Convert signed integer numbers from the decimal system (base ten) to signed binary

How to convert a base ten signed integer number to signed binary:

1) Divide the positive version of number repeatedly by 2, keeping track of each remainder, till we get a quotient that is zero.

2) Construct the base 2 representation by taking the previously calculated remainders starting from the last remainder up to the first one, in that order.

3) Construct the positive binary computer representation so that the first bit is zero.

4) Only if the initial number is negative, change the first bit (the leftmost), from 0 to 1. The leftmost bit is reserved for the sign, 1 = negative, 0 = positive.

Latest signed integers numbers converted from decimal (base ten) to signed binary

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