Binary number and how we can represent a number like 7 (base 10) as a binary num

Question

Binary number and how we can represent a number like 7 (base 10) as a binary number, 0111 (base 2). Now, suppose we’re working in a 4-bit system. This means that we only get to store 4 place values and we have no problem storing “7” as 0111 (base 2). What happens, though if we try to add 7+9 (in the 4-bit system)? We will get 0111+1001=10000, but can not store this extra digit. The result will be 0000 which is clearly not the correct result. This is what is known as “flipping the bit” or “floating point arithmetic errors.” In this discussion we will be talking about these types of issues and practice computation in these number systems.

Regarding two’s complement. Examine the figure above for a 4-bit system.

Q1.)Counting backwards in binary, what happens as we go backwards from 0?

Q2.)Why do the binary representations of +1 and -1 add to zero?

Q3.)Using the circle, can you quickly add 2+3? What about 3-2?

Q4.) The specifics of the method are (1) the first digit represent the sign, (2) the last two digits represent the value. For example, for 1, we have 0001 means 0=positive, 001=1 in base ten. To find the negative value, invert 001 to get 110. Add a 1 to get 111 and then put a 1 in front to signify negative: 1111 is for -1. Check that 2 and -2 work like this too.

Explanation / Answer

For the first questions, you missed specifying the figure.

And checking with the last question:

Check that 2 and -2 work like this too.

For 2, in a 4-bit representation will be 0010.

0 is positive. And 010 = 2 in base ten.

To find negative value, invert 010 to get 101. Add a 1 to get 110 and then put a 1 in front to signify negative: 1110.

If you have any further queries, just get back to me.

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