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  • coding theory - Linear Code, control matrix and leaders tables . . .
    The proper English terms are: (parity) check matrix (not control matrix) and coset (not lateral class) Your check matrix is fine Your syndrome is two bits Your check matrix has all possible non-zero combos of two bits as columns, so it is easy to find coset leaders: place a single one to the position of a column with the desired syndrome (of course, when the syndrome is zero, you have a
  • How do you say $10$ when its in binary? - Mathematics Stack Exchange
    One could read this number as “fifteen”, but that is properly a decimal name for it (five tens), and it gets confusing when one starts reading “1010 0100” as “one hundred sixty two”, which names the number by its decimal representation rather than its binary representation Both digit reading or decimal naming seem wrong
  • binary - Is it an overflow or not? - Mathematics Stack Exchange
    1 1101 + 0100 = 0001 is an overflow if it is a wrong answer and not an overflow if it is a correct answer If these are unsigned binary numbers then 13+4=1 is wrong, so there is an overflow In fact, with unsigned binary, a carry out is always an overflow But you have specified 2s-complement binary
  • Let $S_n$ be the number of binary strings of length = $n$ which do not . . .
    Also, $a_4=12$, because there are 16 strings of length 4 of which we must omit 4, namely, 0100, 0101, 0010, and 1010 Putting $n=4$ into the formula yields $$12= (2) (7)-4+2$$ which is correct, so maybe the answer is right
  • What are the names of numbers in the binary system?
    I agree with this number, but I would like to add the distinction between numbers and digits To tell the digits of a number, you can always say that "three is 'one one' in binary" or "thirty-seven is 'three seven' in decimal" or "twenty is 'A four' in hexadecimal" The individual digits do have names, but they are rarely needed or used; usually you only want to name the numbers The same
  • coding theory - Equivalence of Codes - Mathematics Stack Exchange
    2 Consider the binary codes below: C1= {0000, 1100, 1010, 0110} C2= {0111, 0100, 0010, 0001} C3= {1000, 0100, 0010, 0001} Show that C1 is not equivalent to C3 Is C2 equivalent to C3? When we say two codes are equivalent we mean one can be obtained from the other through repeatedly applying the following two operations to all the codewords:
  • Binary arithmetic - overflow and carryout at same time?
    Overflow and carry out are philosophically the same thing Both indicate that the answer does not fit in the space available The difference is that carry out applies when you have somewhere else to put it, while overflow is when you do not As an example, imagine a four bit computer using unsigned binary for addition If you try to add $1010_2+111_2$ without the word length restriction, you
  • How to subtract BCD numbers? - Mathematics Stack Exchange
    10's complement of 0101 0110 is 0100 0100 (subtracted 9 from each 4 bit segment and added a $1$ to the last one Notice that this could overflow when finding the 10's complement of $0000$
  • How can I convert 2s complement to decimal?
    Suppose I have the 2's complement, negative number 1111 1111 1011 0101 (0xFFBB5) How can I represent this as a decimal number in base 10?
  • truncation in twos complment - Mathematics Stack Exchange
    The four bit two's complement representation of $-4$ is $1100$, which you get by bit complementing $0100$ to get $1011$ then adding one to get $1100$ You are correct that in three bit two's complement notation $100$ is $-4$ decimal You will get proper truncation any time the high order bits are the same down to the first bit you keep, as is the case here





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