I need help with the following questions.
Write each answer as a power of 2. Show your work and explain your steps.
a. Computer capacity is often measured in bits and bytes. A bit is the smallest unit, which is a 1 or 0, in the computer's memory. A byte is 2^3 bits. A megabyte (MB) is 2^20 bytes. How many bits are in a megabyte?
b. A gigabyte (GB) is 2^30 bytes. How many megabytes are in a gigabyte? How many bits are in a gigabyte?
a. 2^3 * 2^20 = 2^23
b. 2^30/2^20 = 2^10
2^30 * 2^3 = ?
a. To find the number of bits in a megabyte (MB), we need to first determine the number of bytes in a megabyte. It is given that a byte is 2^3 bits. Therefore, a megabyte is 2^20 bytes because it is equal to 2^(3*8) bytes.
To convert bytes to bits, we need to multiply the number of bytes by 8 because each byte consists of 8 bits. So, to find the number of bits in a megabyte, we can multiply 2^20 by 8:
2^20 * 8 = 2^(20+3) = 2^23
Therefore, there are 2^23 bits in a megabyte.
b. To find the number of megabytes in a gigabyte (GB), we need to divide the number of bytes in a gigabyte by the number of bytes in a megabyte. It is given that a gigabyte is 2^30 bytes and we know that a megabyte is 2^20 bytes.
To perform the conversion, we can divide the number of bytes in a gigabyte by the number of bytes in a megabyte:
2^30 / 2^20 = 2^(30-20) = 2^10
Therefore, there are 2^10 megabytes in a gigabyte.
To find the number of bits in a gigabyte, we can use the same principle as in part a: multiplying the number of bytes by 8 because each byte consists of 8 bits.
So, to find the number of bits in a gigabyte, we can multiply the number of bytes in a gigabyte (2^30) by 8:
2^30 * 8 = 2^(30+3) = 2^33
Therefore, there are 2^33 bits in a gigabyte.