Base ten decimal system signed integer number 1 011 000 000 001 011 converted to signed binary

How to convert the signed integer in decimal system (in base 10):
1 011 000 000 001 011(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;
  • 1 011 000 000 001 011 ÷ 2 = 505 500 000 000 505 + 1;
  • 505 500 000 000 505 ÷ 2 = 252 750 000 000 252 + 1;
  • 252 750 000 000 252 ÷ 2 = 126 375 000 000 126 + 0;
  • 126 375 000 000 126 ÷ 2 = 63 187 500 000 063 + 0;
  • 63 187 500 000 063 ÷ 2 = 31 593 750 000 031 + 1;
  • 31 593 750 000 031 ÷ 2 = 15 796 875 000 015 + 1;
  • 15 796 875 000 015 ÷ 2 = 7 898 437 500 007 + 1;
  • 7 898 437 500 007 ÷ 2 = 3 949 218 750 003 + 1;
  • 3 949 218 750 003 ÷ 2 = 1 974 609 375 001 + 1;
  • 1 974 609 375 001 ÷ 2 = 987 304 687 500 + 1;
  • 987 304 687 500 ÷ 2 = 493 652 343 750 + 0;
  • 493 652 343 750 ÷ 2 = 246 826 171 875 + 0;
  • 246 826 171 875 ÷ 2 = 123 413 085 937 + 1;
  • 123 413 085 937 ÷ 2 = 61 706 542 968 + 1;
  • 61 706 542 968 ÷ 2 = 30 853 271 484 + 0;
  • 30 853 271 484 ÷ 2 = 15 426 635 742 + 0;
  • 15 426 635 742 ÷ 2 = 7 713 317 871 + 0;
  • 7 713 317 871 ÷ 2 = 3 856 658 935 + 1;
  • 3 856 658 935 ÷ 2 = 1 928 329 467 + 1;
  • 1 928 329 467 ÷ 2 = 964 164 733 + 1;
  • 964 164 733 ÷ 2 = 482 082 366 + 1;
  • 482 082 366 ÷ 2 = 241 041 183 + 0;
  • 241 041 183 ÷ 2 = 120 520 591 + 1;
  • 120 520 591 ÷ 2 = 60 260 295 + 1;
  • 60 260 295 ÷ 2 = 30 130 147 + 1;
  • 30 130 147 ÷ 2 = 15 065 073 + 1;
  • 15 065 073 ÷ 2 = 7 532 536 + 1;
  • 7 532 536 ÷ 2 = 3 766 268 + 0;
  • 3 766 268 ÷ 2 = 1 883 134 + 0;
  • 1 883 134 ÷ 2 = 941 567 + 0;
  • 941 567 ÷ 2 = 470 783 + 1;
  • 470 783 ÷ 2 = 235 391 + 1;
  • 235 391 ÷ 2 = 117 695 + 1;
  • 117 695 ÷ 2 = 58 847 + 1;
  • 58 847 ÷ 2 = 29 423 + 1;
  • 29 423 ÷ 2 = 14 711 + 1;
  • 14 711 ÷ 2 = 7 355 + 1;
  • 7 355 ÷ 2 = 3 677 + 1;
  • 3 677 ÷ 2 = 1 838 + 1;
  • 1 838 ÷ 2 = 919 + 0;
  • 919 ÷ 2 = 459 + 1;
  • 459 ÷ 2 = 229 + 1;
  • 229 ÷ 2 = 114 + 1;
  • 114 ÷ 2 = 57 + 0;
  • 57 ÷ 2 = 28 + 1;
  • 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, by taking all the remainders starting from the bottom of the list constructed above:

1 011 000 000 001 011(10) = 11 1001 0111 0111 1111 1100 0111 1101 1110 0011 0011 1111 0011(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; ...

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:

1 011 000 000 001 011(10) = 0000 0000 0000 0011 1001 0111 0111 1111 1100 0111 1101 1110 0011 0011 1111 0011

Conclusion:

Number 1 011 000 000 001 011, a signed integer, converted from decimal system (base 10) to signed binary:
1 011 000 000 001 011(10) = 0000 0000 0000 0011 1001 0111 0111 1111 1100 0111 1101 1110 0011 0011 1111 0011

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