Converter to signed binary in one's complement representation: converting decimal system (base ten) signed integer numbers

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 on 0 to 1 and all the bits on 1 to 0 (reversing the digits).

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

-77 = 1011 0010 Sep 23 10:45 UTC (GMT)
-4,690 = 1110 1101 1010 1101 Sep 23 10:42 UTC (GMT)
169 = 0000 0000 1010 1001 Sep 23 10:36 UTC (GMT)
-11 = 1111 0100 Sep 23 09:51 UTC (GMT)
-256 = 1111 1110 1111 1111 Sep 23 09:49 UTC (GMT)
-20 = 1110 1011 Sep 23 09:38 UTC (GMT)
-28 = 1110 0011 Sep 23 09:21 UTC (GMT)
-700 = 1111 1101 0100 0011 Sep 23 09:03 UTC (GMT)
10,111 = 0010 0111 0111 1111 Sep 23 08:56 UTC (GMT)
18 = 0001 0010 Sep 23 08:45 UTC (GMT)
158 = 0000 0000 1001 1110 Sep 23 08:31 UTC (GMT)
-65,000 = 1111 1111 1111 1111 0000 0010 0001 0111 Sep 23 08:30 UTC (GMT)
29 = 0001 1101 Sep 23 08:26 UTC (GMT)
All decimal integer numbers converted to signed binary 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