Convert -19 407 144 150 to a signed binary in two's complement representation, from a signed integer number in base 10 decimal system

-19 407 144 150(10) to a signed binary two's complement representation = ?

1. Start with the positive version of the number:

|-19 407 144 150| = 19 407 144 150

2. 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;
  • 19 407 144 150 ÷ 2 = 9 703 572 075 + 0;
  • 9 703 572 075 ÷ 2 = 4 851 786 037 + 1;
  • 4 851 786 037 ÷ 2 = 2 425 893 018 + 1;
  • 2 425 893 018 ÷ 2 = 1 212 946 509 + 0;
  • 1 212 946 509 ÷ 2 = 606 473 254 + 1;
  • 606 473 254 ÷ 2 = 303 236 627 + 0;
  • 303 236 627 ÷ 2 = 151 618 313 + 1;
  • 151 618 313 ÷ 2 = 75 809 156 + 1;
  • 75 809 156 ÷ 2 = 37 904 578 + 0;
  • 37 904 578 ÷ 2 = 18 952 289 + 0;
  • 18 952 289 ÷ 2 = 9 476 144 + 1;
  • 9 476 144 ÷ 2 = 4 738 072 + 0;
  • 4 738 072 ÷ 2 = 2 369 036 + 0;
  • 2 369 036 ÷ 2 = 1 184 518 + 0;
  • 1 184 518 ÷ 2 = 592 259 + 0;
  • 592 259 ÷ 2 = 296 129 + 1;
  • 296 129 ÷ 2 = 148 064 + 1;
  • 148 064 ÷ 2 = 74 032 + 0;
  • 74 032 ÷ 2 = 37 016 + 0;
  • 37 016 ÷ 2 = 18 508 + 0;
  • 18 508 ÷ 2 = 9 254 + 0;
  • 9 254 ÷ 2 = 4 627 + 0;
  • 4 627 ÷ 2 = 2 313 + 1;
  • 2 313 ÷ 2 = 1 156 + 1;
  • 1 156 ÷ 2 = 578 + 0;
  • 578 ÷ 2 = 289 + 0;
  • 289 ÷ 2 = 144 + 1;
  • 144 ÷ 2 = 72 + 0;
  • 72 ÷ 2 = 36 + 0;
  • 36 ÷ 2 = 18 + 0;
  • 18 ÷ 2 = 9 + 0;
  • 9 ÷ 2 = 4 + 1;
  • 4 ÷ 2 = 2 + 0;
  • 2 ÷ 2 = 1 + 0;
  • 1 ÷ 2 = 0 + 1;

3. Construct the base 2 representation of the positive number:

Take all the remainders starting from the bottom of the list constructed above.

19 407 144 150(10) = 100 1000 0100 1100 0001 1000 0100 1101 0110(2)


4. Determine the signed binary number bit length:

The base 2 number's actual length, in bits: 35.

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) indicates the sign,
1 = negative, 0 = positive.

The least number that is:


a power of 2


and is larger than the actual length, 35,


so that the first bit (leftmost) could be zero


(we deal with a positive number at this moment)


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, 64:

19 407 144 150(10) = 0000 0000 0000 0000 0000 0000 0000 0100 1000 0100 1100 0001 1000 0100 1101 0110


6. Get the negative integer number representation. Part 1:

To get the negative integer number representation on 64 bits (8 Bytes),


signed binary one's complement,


replace all the bits on 0 with 1s


and all the bits set on 1 with 0s


(reverse the digits, flip the digits)


!(0000 0000 0000 0000 0000 0000 0000 0100 1000 0100 1100 0001 1000 0100 1101 0110) =


1111 1111 1111 1111 1111 1111 1111 1011 0111 1011 0011 1110 0111 1011 0010 1001


7. Get the negative integer number representation. Part 2:

To get the negative integer number representation on 64 bits (8 Bytes),


signed binary two's complement,


add 1 to the number calculated above


1111 1111 1111 1111 1111 1111 1111 1011 0111 1011 0011 1110 0111 1011 0010 1001 + 1 =


1111 1111 1111 1111 1111 1111 1111 1011 0111 1011 0011 1110 0111 1011 0010 1010


Number -19 407 144 150, a signed integer, converted from decimal system (base 10) to a signed binary two's complement representation:

-19 407 144 150(10) = 1111 1111 1111 1111 1111 1111 1111 1011 0111 1011 0011 1110 0111 1011 0010 1010

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


More operations of this kind:

-19 407 144 151 = ? | -19 407 144 149 = ?


Convert signed integer numbers from the decimal system (base ten) to signed binary two's complement representation

How to convert a base 10 signed integer number to signed binary in two's complement representation:

1) Divide the positive version of number repeatedly by 2, keeping track of each remainder, till getting a quotient that is equal to 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, switch all the bits from 0 to 1 and from 1 to 0 (reversing the digits).

5) Only if the initial number is negative, add 1 to the number at the previous point.

Latest signed integers converted from decimal system to binary two's complement representation

-19,407,144,150 to signed binary two's complement = ? May 06 19:06 UTC (GMT)
-119,999,999,995 to signed binary two's complement = ? May 06 19:06 UTC (GMT)
-52 to signed binary two's complement = ? May 06 19:06 UTC (GMT)
1,011,000,000,001,019 to signed binary two's complement = ? May 06 19:05 UTC (GMT)
-4,215 to signed binary two's complement = ? May 06 19:05 UTC (GMT)
22,732 to signed binary two's complement = ? May 06 19:05 UTC (GMT)
2,147,283,691 to signed binary two's complement = ? May 06 19:05 UTC (GMT)
-13,876 to signed binary two's complement = ? May 06 19:04 UTC (GMT)
1,190,112,520,884,487,206 to signed binary two's complement = ? May 06 19:04 UTC (GMT)
1,050,670 to signed binary two's complement = ? May 06 19:04 UTC (GMT)
1,722 to signed binary two's complement = ? May 06 19:04 UTC (GMT)
1,100,000,110,010,015 to signed binary two's complement = ? May 06 19:04 UTC (GMT)
-503 to signed binary two's complement = ? May 06 19:04 UTC (GMT)
All decimal integer numbers converted to signed binary two's complement representation

How to convert signed integers from decimal system to signed binary in two's complement representation

Follow the steps below to convert a signed base 10 integer number to signed binary in two's complement representation:

  • 1. If the number to be converted is negative, start with the positive version of the number.
  • 2. Divide repeatedly by 2 the positive representation of the integer number, keeping track of each remainder, until 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 must have 4, 8, 16, 32, 64, ... bit length (a power of 2) - if needed, add extra bits on 0 in front (to the left) of the base 2 number above, up to the required length, so that the first bit (the leftmost) will be 0, correctly representing a positive number.
  • 5. To get the negative integer number representation in signed binary one's complement, replace all 0 bits with 1s and all 1 bits with 0s (reversing the digits).
  • 6. To get the negative integer number, in signed binary two's complement representation, add 1 to the number above.

Example: convert the negative number -60 from the decimal system (base ten) to signed binary in two's complement:

  • 1. Start with the positive version of the number: |-60| = 60
  • 2. Divide repeatedly 60 by 2, keeping track of each remainder:
    • division = quotient + remainder
    • 60 ÷ 2 = 30 + 0
    • 30 ÷ 2 = 15 + 0
    • 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:
    60(10) = 11 1100(2)
  • 4. Bit length of base 2 representation number is 6, so the positive binary computer representation of a signed binary will take in this particular case 8 bits (the least power of 2 larger than 6) - add extra 0 digits in front of the base 2 number, up to the required length:
    60(10) = 0011 1100(2)
  • 5. To get the negative integer number representation in signed binary one's complement, replace all the 0 bits with 1s and all 1 bits with 0s (reversing the digits):
    !(0011 1100) = 1100 0011
  • 6. To get the negative integer number, signed binary in two's complement representation, add 1 to the number above:
    -60(10) = 1100 0011 + 1 = 1100 0100
  • Number -60(10), signed integer, converted from decimal system (base 10) to signed binary two's complement representation = 1100 0100