Base ten decimal system signed integer number -1 112 426 078 converted to signed binary in one's complement representation

How to convert a signed integer in decimal system (in base 10):
-1 112 426 078(10)
to a signed binary one's complement representation

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

|-1 112 426 078| = 1 112 426 078

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;
  • 1 112 426 078 ÷ 2 = 556 213 039 + 0;
  • 556 213 039 ÷ 2 = 278 106 519 + 1;
  • 278 106 519 ÷ 2 = 139 053 259 + 1;
  • 139 053 259 ÷ 2 = 69 526 629 + 1;
  • 69 526 629 ÷ 2 = 34 763 314 + 1;
  • 34 763 314 ÷ 2 = 17 381 657 + 0;
  • 17 381 657 ÷ 2 = 8 690 828 + 1;
  • 8 690 828 ÷ 2 = 4 345 414 + 0;
  • 4 345 414 ÷ 2 = 2 172 707 + 0;
  • 2 172 707 ÷ 2 = 1 086 353 + 1;
  • 1 086 353 ÷ 2 = 543 176 + 1;
  • 543 176 ÷ 2 = 271 588 + 0;
  • 271 588 ÷ 2 = 135 794 + 0;
  • 135 794 ÷ 2 = 67 897 + 0;
  • 67 897 ÷ 2 = 33 948 + 1;
  • 33 948 ÷ 2 = 16 974 + 0;
  • 16 974 ÷ 2 = 8 487 + 0;
  • 8 487 ÷ 2 = 4 243 + 1;
  • 4 243 ÷ 2 = 2 121 + 1;
  • 2 121 ÷ 2 = 1 060 + 1;
  • 1 060 ÷ 2 = 530 + 0;
  • 530 ÷ 2 = 265 + 0;
  • 265 ÷ 2 = 132 + 1;
  • 132 ÷ 2 = 66 + 0;
  • 66 ÷ 2 = 33 + 0;
  • 33 ÷ 2 = 16 + 1;
  • 16 ÷ 2 = 8 + 0;
  • 8 ÷ 2 = 4 + 0;
  • 4 ÷ 2 = 2 + 0;
  • 2 ÷ 2 = 1 + 0;
  • 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:

1 112 426 078(10) = 100 0010 0100 1110 0100 0110 0101 1110(2)

4. Determine the signed binary number bit length:

The base 2 number's actual length, in bits: 31.

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 so that the first bit (leftmost) could be zero is: 32.

5. Positive binary computer representation on 32 bits (4 Bytes) - if needed, add extra 0s in front (to the left) of the base 2 number, up to the required length:

1 112 426 078(10) = 0100 0010 0100 1110 0100 0110 0101 1110

6. To get the negative integer number representation on 32 bits (4 Bytes), signed binary one's complement, replace all the bits on 0 with 1s and all the bits set on 1 with 0s (reversing the digits):

!(0100 0010 0100 1110 0100 0110 0101 1110) = 1011 1101 1011 0001 1011 1001 1010 0001

Conclusion:

Number -1 112 426 078, a signed integer, converted from decimal system (base 10) to a signed binary one's complement representation:
-1 112 426 078(10) = 1011 1101 1011 0001 1011 1001 1010 0001

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 one's complement representation

How to convert a base ten signed integer number to signed binary in one's complement representation:

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, switch all the bits from 0 to 1 and all the bits from 1 to 0 (reversing the digits).

Latest signed integers numbers converted from decimal system to signed binary in one's complement representation

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

Follow the steps below to convert a signed base 10 integer number to signed binary in one'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 that is to be converted to binary, keeping track of each remainder, until we get a quotient that is equal to 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, fill in '0' bits in front (to the left) of the base 2 number calculated above, up to the right length; this way the first bit (leftmost) will always 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 '1's and all '1' bits with '0's.

Example: convert the negative number -49 from the decimal system (base ten) to signed binary one's complement:

  • 1. Start with the positive version of the number: |-49| = 49
  • 2. Divide repeatedly 49 by 2, keeping track of each remainder:
    • division = quotient + remainder
    • 49 ÷ 2 = 24 + 1
    • 24 ÷ 2 = 12 + 0
    • 12 ÷ 2 = 6 + 0
    • 6 ÷ 2 = 3 + 0
    • 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:
    49(10) = 11 0001(2)
  • 4. The actual bit length of base 2 representation is 6, so the positive binary computer representation of a signed binary will take in this case 8 bits (the least power of 2 that is larger than 6) - add '0's in front of the base 2 number, up to the required length:
    49(10) = 0011 0001(2)
  • 5. To get the negative integer number representation in signed binary one's complement, replace all '0' bits with '1's and all '1' bits with '0's:
    -49(10) = 1100 1110
  • Number -49(10), signed integer, converted from the decimal system (base 10) to signed binary in one's complement representation = 1100 1110