How many bits can be stored on a 20 GB hard disk? (Hint: 1 GB = 1,073,741,824 bytes; 1 byte = 8 bits.)
The Correct Answer and Explanation is:
To calculate how many bits can be stored on a 20 GB hard disk, we can break the problem down into two parts.
Step 1: Convert gigabytes (GB) to bytes
First, we need to convert the 20 GB to bytes. Given the hint that 1 GB = 1,073,741,824 bytes, we multiply 20 by this value:20 GB=20×1,073,741,824 bytes20 \, \text{GB} = 20 \times 1,073,741,824 \, \text{bytes}20GB=20×1,073,741,824bytes20 GB=21,474,836,480 bytes20 \, \text{GB} = 21,474,836,480 \, \text{bytes}20GB=21,474,836,480bytes
So, 20 GB is equivalent to 21,474,836,480 bytes.
Step 2: Convert bytes to bits
Since 1 byte = 8 bits, we can convert the total number of bytes to bits by multiplying the number of bytes by 8:21,474,836,480 bytes×8 bits per byte=171,798,687,840 bits21,474,836,480 \, \text{bytes} \times 8 \, \text{bits per byte} = 171,798,687,840 \, \text{bits}21,474,836,480bytes×8bits per byte=171,798,687,840bits
Thus, the total number of bits that can be stored on a 20 GB hard disk is 171,798,687,840 bits.
Explanation
The conversion process starts by understanding the basic units of storage. The first step is converting gigabytes to bytes. In computing, storage is often measured in bytes, but because the amount of data we are dealing with is large, we are given the conversion factor for 1 GB in terms of bytes (1 GB = 1,073,741,824 bytes). By multiplying the disk size (20 GB) by the number of bytes in a gigabyte, we arrive at the total byte count.
Next, we convert bytes into bits. A byte is made up of 8 bits, so the total byte count is multiplied by 8 to get the total number of bits. This step gives us the final number, which tells us how much data can be stored on the hard disk in terms of the smallest unit of storage (bits).
This method is useful for understanding how storage capacity translates between different units of measurement in digital storage.
