A modern computer central processing unit chip (CPU) runs with a clock speed of 2.7 GHz. It can execute one operation in each of these clock cycles. (a) how many seconds long is one clock cycle? (b) Electrical signals travel at the speed of light How far can an electrical signal travel in one clock cycles? (c) Wires between the CPUs control unit and its cache memory (both on this chip), are about 2 cm long. How does this compare to how far an electrical signal can travel in one clock cycle?
I was confused because for a I know that v=2.7 GHz and t is what we need to find but I didn't know what d was for the formula v=t/d
time = 1/frequency = 1/(2.7*10^9)
=(1/2.7)* 10^-9 seconds
distance = speed*time
= 3*10^8 *(1/2.7)(10^-9)
= about 0.1 meter = 10 cm
To answer your question, let's break it down step by step:
(a) We are given the clock speed of the CPU, which is 2.7 GHz (gigahertz). This means that the CPU executes 2.7 billion clock cycles per second. To find the duration of one clock cycle, we can use the formula:
v = t / d
Where:
v = velocity (speed)
t = time (duration)
d = distance
In this case, the speed (v) is given by the clock speed of the CPU (2.7 GHz). We want to find the duration (t), so we rearrange the formula:
t = d / v
Since we're looking for the length of one clock cycle (t), we substitute the distance (d) as 1 (since we're interested in the length of one cycle) and the velocity (v) as 2.7 GHz.
t = 1 / 2.7 GHz
To convert gigahertz to seconds, we use the fact that 1 GHz = 1 billion cycles per second. Therefore, 2.7 GHz = 2.7 billion cycles per second.
t = 1 / 2.7 billion seconds
Hence, one clock cycle is approximately 0.37 nanoseconds long.
(b) Electrical signals travel at the speed of light, which is approximately 299,792 kilometers per second. To calculate how far an electrical signal can travel in one clock cycle, we need to multiply the speed of light by the duration of one clock cycle:
distance = speed * time
distance = 299,792 km/s * 0.37 ns
To convert nanoseconds to seconds, we divide by 1 billion (1 ns = 1 billionth of a second):
distance = 299,792 km/s * 0.37 / 1 billion s
Hence, an electrical signal can travel approximately 0.111 kilometers (or 111 meters) in one clock cycle.
(c) The wires between the CPU's control unit and its cache memory on the chip are about 2 cm long. Comparing this length to how far an electrical signal can travel in one clock cycle, we can see that the length of the wires is much smaller. An electrical signal can travel approximately 111 meters in one clock cycle, which is much longer than the 2 cm distance of the wires.
In summary:
(a) One clock cycle is approximately 0.37 nanoseconds long.
(b) An electrical signal can travel approximately 111 meters in one clock cycle.
(c) The wires on the chip are about 2 cm long, which is significantly smaller than the distance an electrical signal can travel in one clock cycle.
To answer these questions, let's break it down step by step.
(a) How many seconds long is one clock cycle?
Clock speed is often measured in hertz (Hz), where 1 Hz corresponds to one cycle per second. In this case, the CPU has a clock speed of 2.7 GHz. "G" represents gigahertz, which means billion cycles per second.
To calculate the duration of one clock cycle, we can use the formula:
t = 1 / f
where t is the time (in seconds) and f is the frequency (in hertz). In this case, the frequency (f) is 2.7 GHz.
Converting 2.7 GHz to hertz:
2.7 GHz = 2.7 × 10^9 Hz
Now, we can calculate the duration of one clock cycle:
t = 1 / (2.7 × 10^9 Hz)
(b) How far can an electrical signal travel in one clock cycle?
To determine how far an electrical signal can travel in one clock cycle, we need to know the speed at which the signal propagates. The speed of light is often used as an approximation since electrical signals in wires travel close to the speed of light.
The speed of light (c) is approximately 3 × 10^8 meters per second.
To find the distance traveled by an electrical signal in one clock cycle, we multiply the speed of light by the duration of one clock cycle:
d = c × t
Substituting the value of "t" we calculated in part (a), we can determine the distance traveled:
d = (3 × 10^8 m/s) × t
(c) Comparing the wire length to the distance an electrical signal can travel in one clock cycle:
In this case, the wires between the CPU's control unit and cache memory are approximately 2 cm long. To compare it to the distance an electrical signal can travel in one clock cycle, we can use the values we calculated in parts (a) and (b).
If the distance traveled by an electrical signal in one clock cycle (d) is shorter than the wire's length (2 cm), then the signal can easily travel through the wire within one clock cycle. If it is longer, the signal would not be able to cover the entire wire length within that time.
Now, you have the formulas and information needed to calculate the answers to these questions. Use the equations provided, substitute the values, and solve for the unknown variables.