Integer as Two's Complement Binary: Number 281 474 979 999 974 Converted and Written as a Signed Binary in Two's Complement Representation

Integer number 281 474 979 999 974(10) written as a signed binary in two's complement representation

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;
  • 281 474 979 999 974 ÷ 2 = 140 737 489 999 987 + 0;
  • 140 737 489 999 987 ÷ 2 = 70 368 744 999 993 + 1;
  • 70 368 744 999 993 ÷ 2 = 35 184 372 499 996 + 1;
  • 35 184 372 499 996 ÷ 2 = 17 592 186 249 998 + 0;
  • 17 592 186 249 998 ÷ 2 = 8 796 093 124 999 + 0;
  • 8 796 093 124 999 ÷ 2 = 4 398 046 562 499 + 1;
  • 4 398 046 562 499 ÷ 2 = 2 199 023 281 249 + 1;
  • 2 199 023 281 249 ÷ 2 = 1 099 511 640 624 + 1;
  • 1 099 511 640 624 ÷ 2 = 549 755 820 312 + 0;
  • 549 755 820 312 ÷ 2 = 274 877 910 156 + 0;
  • 274 877 910 156 ÷ 2 = 137 438 955 078 + 0;
  • 137 438 955 078 ÷ 2 = 68 719 477 539 + 0;
  • 68 719 477 539 ÷ 2 = 34 359 738 769 + 1;
  • 34 359 738 769 ÷ 2 = 17 179 869 384 + 1;
  • 17 179 869 384 ÷ 2 = 8 589 934 692 + 0;
  • 8 589 934 692 ÷ 2 = 4 294 967 346 + 0;
  • 4 294 967 346 ÷ 2 = 2 147 483 673 + 0;
  • 2 147 483 673 ÷ 2 = 1 073 741 836 + 1;
  • 1 073 741 836 ÷ 2 = 536 870 918 + 0;
  • 536 870 918 ÷ 2 = 268 435 459 + 0;
  • 268 435 459 ÷ 2 = 134 217 729 + 1;
  • 134 217 729 ÷ 2 = 67 108 864 + 1;
  • 67 108 864 ÷ 2 = 33 554 432 + 0;
  • 33 554 432 ÷ 2 = 16 777 216 + 0;
  • 16 777 216 ÷ 2 = 8 388 608 + 0;
  • 8 388 608 ÷ 2 = 4 194 304 + 0;
  • 4 194 304 ÷ 2 = 2 097 152 + 0;
  • 2 097 152 ÷ 2 = 1 048 576 + 0;
  • 1 048 576 ÷ 2 = 524 288 + 0;
  • 524 288 ÷ 2 = 262 144 + 0;
  • 262 144 ÷ 2 = 131 072 + 0;
  • 131 072 ÷ 2 = 65 536 + 0;
  • 65 536 ÷ 2 = 32 768 + 0;
  • 32 768 ÷ 2 = 16 384 + 0;
  • 16 384 ÷ 2 = 8 192 + 0;
  • 8 192 ÷ 2 = 4 096 + 0;
  • 4 096 ÷ 2 = 2 048 + 0;
  • 2 048 ÷ 2 = 1 024 + 0;
  • 1 024 ÷ 2 = 512 + 0;
  • 512 ÷ 2 = 256 + 0;
  • 256 ÷ 2 = 128 + 0;
  • 128 ÷ 2 = 64 + 0;
  • 64 ÷ 2 = 32 + 0;
  • 32 ÷ 2 = 16 + 0;
  • 16 ÷ 2 = 8 + 0;
  • 8 ÷ 2 = 4 + 0;
  • 4 ÷ 2 = 2 + 0;
  • 2 ÷ 2 = 1 + 0;
  • 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.

281 474 979 999 974(10) = 1 0000 0000 0000 0000 0000 0000 0011 0010 0011 0000 1110 0110(2)

3. Determine the signed binary number bit length:

The base 2 number's actual length, in bits: 49.


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; ...


The first bit (the leftmost) indicates the sign:

0 = positive integer number, 1 = negative integer number


The least number that is:


1) a power of 2

2) and is larger than the actual length, 49,

3) so that the first bit (leftmost) could be zero
(we deal with a positive number at this moment)


=== is: 64.


4. Get the 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.


Number 281 474 979 999 974(10), a signed integer number (with sign), converted from decimal system (from base 10) and written as a signed binary in two's complement representation:

281 474 979 999 974(10) = 0000 0000 0000 0001 0000 0000 0000 0000 0000 0000 0011 0010 0011 0000 1110 0110

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

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