Base ten decimal system signed integer number -8 157 989 228 746 813 600 converted to signed binary

How to convert the signed integer in decimal system (in base 10):
-8 157 989 228 746 813 600(10)
to a signed binary

1. We start with the positive version of the number:

|-8 157 989 228 746 813 600| = 8 157 989 228 746 813 600

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

  • division = quotient + remainder;
  • 8 157 989 228 746 813 600 ÷ 2 = 4 078 994 614 373 406 800 + 0;
  • 4 078 994 614 373 406 800 ÷ 2 = 2 039 497 307 186 703 400 + 0;
  • 2 039 497 307 186 703 400 ÷ 2 = 1 019 748 653 593 351 700 + 0;
  • 1 019 748 653 593 351 700 ÷ 2 = 509 874 326 796 675 850 + 0;
  • 509 874 326 796 675 850 ÷ 2 = 254 937 163 398 337 925 + 0;
  • 254 937 163 398 337 925 ÷ 2 = 127 468 581 699 168 962 + 1;
  • 127 468 581 699 168 962 ÷ 2 = 63 734 290 849 584 481 + 0;
  • 63 734 290 849 584 481 ÷ 2 = 31 867 145 424 792 240 + 1;
  • 31 867 145 424 792 240 ÷ 2 = 15 933 572 712 396 120 + 0;
  • 15 933 572 712 396 120 ÷ 2 = 7 966 786 356 198 060 + 0;
  • 7 966 786 356 198 060 ÷ 2 = 3 983 393 178 099 030 + 0;
  • 3 983 393 178 099 030 ÷ 2 = 1 991 696 589 049 515 + 0;
  • 1 991 696 589 049 515 ÷ 2 = 995 848 294 524 757 + 1;
  • 995 848 294 524 757 ÷ 2 = 497 924 147 262 378 + 1;
  • 497 924 147 262 378 ÷ 2 = 248 962 073 631 189 + 0;
  • 248 962 073 631 189 ÷ 2 = 124 481 036 815 594 + 1;
  • 124 481 036 815 594 ÷ 2 = 62 240 518 407 797 + 0;
  • 62 240 518 407 797 ÷ 2 = 31 120 259 203 898 + 1;
  • 31 120 259 203 898 ÷ 2 = 15 560 129 601 949 + 0;
  • 15 560 129 601 949 ÷ 2 = 7 780 064 800 974 + 1;
  • 7 780 064 800 974 ÷ 2 = 3 890 032 400 487 + 0;
  • 3 890 032 400 487 ÷ 2 = 1 945 016 200 243 + 1;
  • 1 945 016 200 243 ÷ 2 = 972 508 100 121 + 1;
  • 972 508 100 121 ÷ 2 = 486 254 050 060 + 1;
  • 486 254 050 060 ÷ 2 = 243 127 025 030 + 0;
  • 243 127 025 030 ÷ 2 = 121 563 512 515 + 0;
  • 121 563 512 515 ÷ 2 = 60 781 756 257 + 1;
  • 60 781 756 257 ÷ 2 = 30 390 878 128 + 1;
  • 30 390 878 128 ÷ 2 = 15 195 439 064 + 0;
  • 15 195 439 064 ÷ 2 = 7 597 719 532 + 0;
  • 7 597 719 532 ÷ 2 = 3 798 859 766 + 0;
  • 3 798 859 766 ÷ 2 = 1 899 429 883 + 0;
  • 1 899 429 883 ÷ 2 = 949 714 941 + 1;
  • 949 714 941 ÷ 2 = 474 857 470 + 1;
  • 474 857 470 ÷ 2 = 237 428 735 + 0;
  • 237 428 735 ÷ 2 = 118 714 367 + 1;
  • 118 714 367 ÷ 2 = 59 357 183 + 1;
  • 59 357 183 ÷ 2 = 29 678 591 + 1;
  • 29 678 591 ÷ 2 = 14 839 295 + 1;
  • 14 839 295 ÷ 2 = 7 419 647 + 1;
  • 7 419 647 ÷ 2 = 3 709 823 + 1;
  • 3 709 823 ÷ 2 = 1 854 911 + 1;
  • 1 854 911 ÷ 2 = 927 455 + 1;
  • 927 455 ÷ 2 = 463 727 + 1;
  • 463 727 ÷ 2 = 231 863 + 1;
  • 231 863 ÷ 2 = 115 931 + 1;
  • 115 931 ÷ 2 = 57 965 + 1;
  • 57 965 ÷ 2 = 28 982 + 1;
  • 28 982 ÷ 2 = 14 491 + 0;
  • 14 491 ÷ 2 = 7 245 + 1;
  • 7 245 ÷ 2 = 3 622 + 1;
  • 3 622 ÷ 2 = 1 811 + 0;
  • 1 811 ÷ 2 = 905 + 1;
  • 905 ÷ 2 = 452 + 1;
  • 452 ÷ 2 = 226 + 0;
  • 226 ÷ 2 = 113 + 0;
  • 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;

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

8 157 989 228 746 813 600(10) = 111 0001 0011 0110 1111 1111 1111 1011 0000 1100 1110 1010 1011 0000 1010 0000(2)

4. Determine the signed binary number bit length:

The base 2 number's actual length, in bits: 63.

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.

5. 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:

8 157 989 228 746 813 600(10) = 0111 0001 0011 0110 1111 1111 1111 1011 0000 1100 1110 1010 1011 0000 1010 0000

6. To get the negative integer number representation change the first bit (the leftmost), from 0 to 1:

-8 157 989 228 746 813 600(10) = 1111 0001 0011 0110 1111 1111 1111 1011 0000 1100 1110 1010 1011 0000 1010 0000

Conclusion:

Number -8 157 989 228 746 813 600, a signed integer, converted from decimal system (base 10) to signed binary:
-8 157 989 228 746 813 600(10) = 1111 0001 0011 0110 1111 1111 1111 1011 0000 1100 1110 1010 1011 0000 1010 0000

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