Answer
a)1
b) 2
c) 63
d) 375
Work Step by Step
(a) Given: n = 4 bits
The number of bytes corresponding to n bits is then the number of bits
divided by 8 (since a byte is a group of 8 bits)
However the number of bytes always has to be an not an integer, thus if the result is not an integer, then we need to round the decimal up to the nearest integer (which corresponds to the ceiling function).
$$\lceil{n/8}\rceil=\lceil{4/8}\rceil=\lceil{0.5}\rceil=1$$
(b) Given: n = 10 bits
The number of bytes corresponding to n bits is then the number of bits
divided by 8 (since a byte is a group of 8 bits)
However the number of bytes always has to be an not an integer, thus if the result is not an integer, then we need to round the decimal up to the nearest integer (which corresponds to the ceiling function).
$$\lceil{n/8}\rceil=\lceil{10/8}\rceil=\lceil{5/4}\rceil=\lceil{1.25}\rceil=2$$
(c) Given: n = 500 bits
The number of bytes corresponding to n bits is then the number of bits
divided by 8 (since a byte is a group of 8 bits)
However the number of bytes always has to be an not an integer, thus if the result is not an integer, then we need to round the decimal up to the nearest integer (which corresponds to the ceiling function).
$$\lceil{n/8}\rceil=\lceil{500/8}\rceil=\lceil{125/2}\rceil=\lceil{62.5}\rceil=63$$
(d) Given: n = 3000 bits
The number of bytes corresponding to n bits is then the number of bits
divided by 8 (since a byte is a group of 8 bits)
However the number of bytes always has to be an not an integer, thus if the result is not an integer, then we need to round the decimal up to the nearest integer (which corresponds to the ceiling function).
$$\lceil{n/8}\rceil=\lceil{3000/8}\rceil=\lceil{375}\rceil=375$$
