Number systems：練習問題

An 8-bit register contains the binary value \(00111100_2\). What is the result in binary after a logical right shift of 3 places is performed?

What is the hexadecimal representation of the denary number \(455\)?

A computer uses 8-bit registers to store positive integers. What is the result of the following binary addition?

\(10101100_2 + 01100011_2\)

In the context of computer data representation, how many bits of information are represented by the hexadecimal value \(C4_{16}\)?

A CPU uses 8-bit registers to store positive integers. It attempts to add the binary numbers \(11110000_2\) and \(00010101_2\).
Which statement correctly describes the result of this operation?

Convert the 8-bit binary number \(11100101_2\) into its equivalent hexadecimal representation.

Convert the denary number 219 into its equivalent hexadecimal representation.

Calculate the 8-bit binary addition of \(10011000_2\) and \(11001101_2\). Explain why the resulting value would cause an overflow error in an 8-bit register.

a) Convert the binary number $$11010110_2$$ to its denary (base 10) equivalent.

b) An 8-bit register stores the positive binary number $$10110100_2$$. Another 8-bit register stores $$01001101_2$$. Perform the binary addition of these two numbers and state the result in 8-bit binary. Convert the 8-bit binary sum to its denary equivalent. Indicate if an overflow error occurs and explain why.

An 8-bit CPU performs addition on two positive binary integers stored in its registers.

Register 1: \( 01010101_2 \)
Register 2: \( 10101011_2 \)

a) Calculate the binary sum of the values in Register 1 and Register 2. Show your working. [2]
b) Convert the resulting binary sum into its denary equivalent. [2]
c) Explain why the CPU would flag an error if it attempted to store the result of the denary calculation \( 200 + 100 \) in a single 8-bit register. [1]