Convert 1 000 000 000 101 018 to signed binary, from a base 10 decimal system signed integer number

1 000 000 000 101 018(10) to a signed binary = ?

1. Divide the number repeatedly by 2:

Keep track of each remainder.

We stop when we get a quotient that is equal to zero.

  • division = quotient + remainder;
  • 1 000 000 000 101 018 ÷ 2 = 500 000 000 050 509 + 0;
  • 500 000 000 050 509 ÷ 2 = 250 000 000 025 254 + 1;
  • 250 000 000 025 254 ÷ 2 = 125 000 000 012 627 + 0;
  • 125 000 000 012 627 ÷ 2 = 62 500 000 006 313 + 1;
  • 62 500 000 006 313 ÷ 2 = 31 250 000 003 156 + 1;
  • 31 250 000 003 156 ÷ 2 = 15 625 000 001 578 + 0;
  • 15 625 000 001 578 ÷ 2 = 7 812 500 000 789 + 0;
  • 7 812 500 000 789 ÷ 2 = 3 906 250 000 394 + 1;
  • 3 906 250 000 394 ÷ 2 = 1 953 125 000 197 + 0;
  • 1 953 125 000 197 ÷ 2 = 976 562 500 098 + 1;
  • 976 562 500 098 ÷ 2 = 488 281 250 049 + 0;
  • 488 281 250 049 ÷ 2 = 244 140 625 024 + 1;
  • 244 140 625 024 ÷ 2 = 122 070 312 512 + 0;
  • 122 070 312 512 ÷ 2 = 61 035 156 256 + 0;
  • 61 035 156 256 ÷ 2 = 30 517 578 128 + 0;
  • 30 517 578 128 ÷ 2 = 15 258 789 064 + 0;
  • 15 258 789 064 ÷ 2 = 7 629 394 532 + 0;
  • 7 629 394 532 ÷ 2 = 3 814 697 266 + 0;
  • 3 814 697 266 ÷ 2 = 1 907 348 633 + 0;
  • 1 907 348 633 ÷ 2 = 953 674 316 + 1;
  • 953 674 316 ÷ 2 = 476 837 158 + 0;
  • 476 837 158 ÷ 2 = 238 418 579 + 0;
  • 238 418 579 ÷ 2 = 119 209 289 + 1;
  • 119 209 289 ÷ 2 = 59 604 644 + 1;
  • 59 604 644 ÷ 2 = 29 802 322 + 0;
  • 29 802 322 ÷ 2 = 14 901 161 + 0;
  • 14 901 161 ÷ 2 = 7 450 580 + 1;
  • 7 450 580 ÷ 2 = 3 725 290 + 0;
  • 3 725 290 ÷ 2 = 1 862 645 + 0;
  • 1 862 645 ÷ 2 = 931 322 + 1;
  • 931 322 ÷ 2 = 465 661 + 0;
  • 465 661 ÷ 2 = 232 830 + 1;
  • 232 830 ÷ 2 = 116 415 + 0;
  • 116 415 ÷ 2 = 58 207 + 1;
  • 58 207 ÷ 2 = 29 103 + 1;
  • 29 103 ÷ 2 = 14 551 + 1;
  • 14 551 ÷ 2 = 7 275 + 1;
  • 7 275 ÷ 2 = 3 637 + 1;
  • 3 637 ÷ 2 = 1 818 + 1;
  • 1 818 ÷ 2 = 909 + 0;
  • 909 ÷ 2 = 454 + 1;
  • 454 ÷ 2 = 227 + 0;
  • 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.

1 000 000 000 101 018(10) = 11 1000 1101 0111 1110 1010 0100 1100 1000 0000 1010 1001 1010(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, 50,


so that the first bit (leftmost) could be zero


(we deal with a positive number at this moment)


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, 64:

1 000 000 000 101 018(10) = 0000 0000 0000 0011 1000 1101 0111 1110 1010 0100 1100 1000 0000 1010 1001 1010


Number 1 000 000 000 101 018, a signed integer, converted from decimal system (base 10) to signed binary:

1 000 000 000 101 018(10) = 0000 0000 0000 0011 1000 1101 0111 1110 1010 0100 1100 1000 0000 1010 1001 1010

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

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


More operations of this kind:

1 000 000 000 101 017 = ? | Signed integer 1 000 000 000 101 019 = ?


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

How to convert a base 10 signed integer number to signed binary:

1) Divide the positive version of number repeatedly by 2, keeping track of each remainder, till getting a quotient that is 0.

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 0.

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 integer numbers in decimal (base ten) converted to signed binary

1,000,000,000,101,018 to signed binary = ? Jul 24 11:38 UTC (GMT)
49,415 to signed binary = ? Jul 24 11:38 UTC (GMT)
100,111,100 to signed binary = ? Jul 24 11:38 UTC (GMT)
-733,307,779,761,753,298 to signed binary = ? Jul 24 11:38 UTC (GMT)
29,890 to signed binary = ? Jul 24 11:37 UTC (GMT)
-1,121,911 to signed binary = ? Jul 24 11:37 UTC (GMT)
11,109,991 to signed binary = ? Jul 24 11:37 UTC (GMT)
9,779 to signed binary = ? Jul 24 11:37 UTC (GMT)
1,234,551,233,465,119 to signed binary = ? Jul 24 11:37 UTC (GMT)
21,184 to signed binary = ? Jul 24 11:37 UTC (GMT)
4,448 to signed binary = ? Jul 24 11:37 UTC (GMT)
-76,984 to signed binary = ? Jul 24 11:36 UTC (GMT)
540,237 to signed binary = ? Jul 24 11:36 UTC (GMT)
All decimal positive integers converted 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