What is the binary form of -10? How it is calculated?
+3
A:
Take the binary form of 10, invert all the bits, and add one.
10 0000 1010 invert 1111 0101 add 1 1111 0110
Ignacio Vazquez-Abrams
2010-01-29 05:20:37
Refer to two's complement: http://en.wikipedia.org/wiki/Twos_complement
Lytol
2010-01-29 05:24:44
Assuming twos complement and no overflow.
David Lively
2010-01-29 05:25:52
Your answer is correct for an 8-bit cell. What about a 4-bit or 16-bit cell?
Brandon
2010-01-29 05:30:15
thanks for answer. yes what about 4 bit cell ?
Dinesh
2010-01-29 05:37:33
@Brandon: The answer is correct regardless of word size; it just so happens that 10 will overflow a signed 4-bit word.
Ignacio Vazquez-Abrams
2010-01-29 05:38:25
+3
A:
Follow this link. You can find the binary form of a negative number say -n by finding out the two's complement of n.
Prasoon Saurav
2010-01-29 05:23:01
You're assuming two's complement. There is no "the" binary form of a negative number.
Alok
2010-01-29 06:46:09
+4
A:
To convert -10 (decimal) to binary:
Repeatedly divide the absolute value (|-10| = 10) of the number by 2 until you get 0 in the quotient:
(10 / 2 = 5 R 0)
(5 / 2 = 2 R 1)
(2 / 2 = 1 R 0)
(1 / 2 = 0 R 1) // zero is the value in the quotient so we stop dividing
Place the remainders in order to obtain the binary equivalent:
1010
For an 8-bit cell the answer is 0000 1010, 16-bit cell 0000 0000 0000 1010, and so on.
Take the one's complement by inverting the bits (we will assume an 8-bit cell holds the final value):
0000 1010
1111 0101 // bits are inverted
Now take the 2's complement by adding 1:
1111 0101
+ 1
----------
1111 0110 // final answer
What happens with a 4-bit cell?
The one's complement would be:
1010
0101 // inverted bits
Taking the 2's complement produces:
0101
+ 1
----
0110 // final answer for a 4-bit cell
Since the number should be negative and the result does not indicate that (the number begins with 0 when it should begin with a 1) an overflow condition would occur.
Brandon
2010-01-29 05:48:28
very detailed +1. You might want to mention Big/Little Endian too.
Johannes Rudolph
2010-01-29 05:52:18
@Johannes: Endianness doesn't come into picture when talking about binary representations. That's only significant when > 1 byte is stored in a computer. @Brandon: nit: it's **ones'** complement, not **one's**.
Alok
2010-01-29 06:30:36
@Johannes: Again, that comes into the picture only when storing a number in memory. It's equivalent to saying that the number "one thousand, two hundred and thirty four" has the representations 1234 or 4321 based upon endianness. The number has only one representation, it's only when we're storing it in memory do we talk about endianness.
Alok
2010-01-29 06:57:04