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How to subtract the hexadecimal number 1245 from D257 using two's complement addition method?
You take 1245 and form the two's complement of it then add it to D257. The two's complement of a number is defined as the 1's complement + 1. In signed two's complement arithmetic, the most significant bit is the "sign" bit. 1 indicates a negative number and 0 indicates a positive number. To find the magnitude of a negative number, take it's two's complement (ignoring carry bits). To get the two's complement of 1245, take the 1's complement of 1245 and add 1. In binary 1245 is 0001001001000101. The one's complement is 1110110110111010 (in hex that's EDBA) . Adding 1 to this will give you the two's complement. That is EDBA+0001 (ignore the carry if any), is EDBB. Now you add EDBB to D257 and ignore any carry, so that will be 1C012 (throw away the carry bit), C012. C012 is a negative number (the sign bit, the most significant bit, is 1). To find its magnitude, apply the two's complement algorithm above, and you'll find it to be -16365. Note: D257 is a negative number, and you're subracting a positive number, so you're going to end up with another negative number, i.e. adding the two's complement of a number is the same thing as subtracting the number. You can check your result by doing the math in decimal to see if it adds up. D257 in decimal = -11688 (you apply the two's complement to the number to find the magnitude, and the sign is negative because the sign bit, the most signficant bit is 1). 1245 in decimal = 4677. -11688-4677 = -16365 (which in hex signed two's complement is C012).
The IEE standared 32 bit floating point representation of the binary number 19.5 is?
0 10000011 11100000000000000000000
What differencess between one's complement and two's complement?
one's complement is a bitwise complement of a binary number. (ie, 1 becomes 0 and 0 becomes 1) A one's complement isn't really used as much as a two's complement. A two's complement is used in a system where the larges bit in a binary number represents a negative number. so the bits for a 4 bit number would have the values of (from right to left): -8, 4, 2, 1 this allows you to represent any number from -8 (1000) to positive 7 (0111) To find the two's complement of a number, you take the one's complement, and then add 1. This significant because if a computer wants to subtract two numbers, it simply takes the two's complement of the second number and adds them together. More significance arises in digital circuits when constructing circuits using only nand/nor gates, as these perform slightly faster than and/or gates.
A 1 or 0 in the binary number system is called?
A 0 or 1 in a binary number is called a bit. A binary number is made up of only ones and zeroes.
1's complement of 1000?
Ones complement simply switches the state of all the bits (0s becomes 1s and 1s becomes 0s). Assuming 1000 is binary (for decimal 8), the 1's complement would be 0111. But if 1000 is really decimal one thousand, the binary equivalent would 1111101000, thus the ones complement would be 0000010111. Ones complement was originally used to represent signed integers. To flip the sign, all bits were flipped and the most-significant bit denoted the sign (0 for positive, 1 for negative). The problem with one's complement is that we end with two representations for the value zero: 00000000 and 11111111 in 8-bit notation. To eliminate this, most modern systems now use twos complement, which is ones complement plus one. Thus 00000000 is 11111111 + 00000001 which is 00000000. Note that ones complement notation means that an 8-bit value has a valid range of -127 through +127 (with two representations for zero) while twos complement gives us a range of -128 through +127. Signed integer notation is also system-dependent, hence the reason why a char data type in C only has a guaranteed range of at least -127 through +127 across all implementations. For that reason it is not safe to assume that -128 has a valid representation in 8-bit signed notation across all implementations.
