Question

In a given byte-addressable computer, memory locations \(10000 \mathrm{H}\) to \(9 \mathrm{FFFFH}\) are available for user programs. The first location is \(10000 \mathrm{H}\) and the last location is 9FFFFH. Calculate the following: (a) The total number of bytes available (in decimal) (b) The total number of kilobytes (in decimal)

Short answer

There are 638976 bytes available, which is equivalent to 624 kilobytes (in decimal).

Step-by-step solution

Converting Hexadecimal Addresses to Decimal

Convert the starting and ending addresses from hexadecimal to decimal. The hexadecimal number system is base-16, and each digit represents a power of 16. Convert the hexadecimal addresses '10000H' and '9FFFFH' into their decimal equivalents.

Calculate the Total Number of Addresses

Find the total number of addresses by subtracting the starting address decimal value from the ending address decimal value and then adding 1. This is because the range is inclusive of both the starting and ending addresses.

Convert Bytes to Kilobytes

To convert bytes to kilobytes, divide the total number of bytes by 1024, since one kilobyte is equal to 1024 bytes.

Key concepts

Hexadecimal to Decimal Conversion

Understanding the conversion from hexadecimal to decimal is crucial when dealing with computer memory, as addresses are often represented in a hexadecimal format. Hexadecimal is a base-16 number system, which means it includes sixteen distinct symbols: 0-9 to represent values zero to nine, and A-F to represent values ten to fifteen. To convert a hexadecimal number to decimal, you first need to understand the place value of each digit. The rightmost digit represents the 'ones' place, and as you move left, the place value of each digit increases by a power of sixteen.

For a hexadecimal number like '9FFFFH', we start from the rightmost digit (which is represented by 'H' to signify hexadecimal), and each digit to the left is a higher power of 16. Using the formula: Decimal = (Digit * 16^position) (starting from position 0 from the right), we can convert any hexadecimal address to its decimal equivalent. It's important to note that letters A through F translate to numbers 10 through 15. This conversion allows us to manipulate and understand memory addresses in a numerical format that's more familiar to most individuals.

Memory Addressing

In computer systems, memory addressing refers to the scheme by which bytes of memory are mapped to memory addresses that the processor can use to access data. Each unique address refers to a different byte in memory. When we say that a computer's memory is byte-addressable, it means that each unique memory address corresponds to one byte of storage. This is critical for understanding the range of usable memory in a system.

In the exercise, the address range for user programs is from '10000H' to '9FFFFH', which indicates that each memory location between these addresses can store one byte of data. When calculating the total memory available, you subtract the lower address from the higher one and add one to account for the range being inclusive. Remember, this range tells us how much data—or how many bytes—the user programs can utilize in this system.

Bytes to Kilobytes Conversion

Knowing how to convert bytes to kilobytes is essential for understanding the size of data in a context larger than individual characters or symbols. Since computers operate with binary data, sizes are generally expressed in powers of 2. A kilobyte is defined as 1024 bytes (which is 2^10), reflecting this binary system. To convert bytes into kilobytes, you divide the total number of bytes by 1024. This is a common operation when assessing memory requirements or capacities in computing.

For example, if a system has 2048 bytes of memory, dividing by 1024 results in 2 kilobytes. This conversion is often seen in everyday computing scenarios, like when checking the size of files or storage devices where larger units like kilobytes, megabytes, or gigabytes are more appropriate and easier to comprehend than a vast number of bytes.