- #1
naspek
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Homework Statement
Perform the following arithmetic operation using 8-bit
two's complement
a) 8710 - 2910
The Attempt at a Solution
i just want to know.. am i converting the number correctly?
89 = 0101 1001
-29 = 1110 0011
One quibble: you wrote 87 above, but worked with 89 below.naspek said:Homework Statement
Perform the following arithmetic operation using 8-bit
two's complement
a) 8710 - 2910
naspek said:The Attempt at a Solution
i just want to know.. am i converting the number correctly?
89 = 0101 1001
-29 = 1110 0011
Two's complement is a method of representing signed numbers in binary form. It involves flipping the bits of a number and adding 1 to the result to get the negative equivalent of the original number. This allows for efficient arithmetic operations on both positive and negative numbers.
In 8-bit arithmetic, two's complement is used to represent both positive and negative numbers within a range of -128 to 127. This is achieved by reserving the first bit (also known as the sign bit) as the indicator of the number's sign. A value of 0 in the sign bit represents a positive number, while a value of 1 represents a negative number.
The use of two's complement in arithmetic operations allows for the addition, subtraction, and multiplication of both positive and negative numbers without the need for separate algorithms for each operation. This simplifies the process and reduces the amount of code needed to perform these operations.
No, two's complement cannot be used for division in 8-bit arithmetic. This is because two's complement is not a reversible operation, meaning that it cannot be used to accurately represent fractions or decimals. For division, a different method called "signed magnitude" is used.
Yes, there are some limitations to using two's complement in 8-bit arithmetic. One limitation is that the range of numbers that can be represented is limited to -128 to 127. Additionally, because the first bit is reserved as the sign bit, there are fewer bits available for representing the magnitude of the number, which can result in less precision compared to other methods of representing numbers.