Question

In a system with 16GB, external fragmentation requires

that we compact memory to fill in the holes. We need to

copy three fourths of memory from one location to another.

Assuming a 256-bit data bus with a system clock of 1GHz

that requires 50 clocks per read and write, how long will

it take for this operation to complete? Remember the

relationship between powers of 2 and 10 and don’t worry

about conversion errors.

Answer 1

Total memory of system, M_T = 16 GB

M_T = 2⁴GB = 2⁴ * 2³⁰

M_T = 2³⁴b // 'b' stands for 'bits'

Amount of memory that we need to copy from one location to other location,

M_C = (3/4) * 16GB

M_C = 12GB

M_C = 12 * 2³⁰b // 'b' stands for 'bits'

Our data bus size is 256 bits, so we can transfer 256 bits of data at once from one location to other location.

So, we have 'M_C' amount of data to transfer using 256 bits size data bus, hence total number of reads required are,

R_T = M_C/256

R_T = 12 * 2³⁰/2⁸

R_T = 12 * 2²²

1 read takes 50 clock cycles, so R_T​​​​​​​ reads will take,

CC = 50 * 12 * 2²²

CC = 600 * 2²²

'CC' clock cycles will be required to copy required size memory area from one place and same number of CC cycles will be required to write this memory area onto other place.

so total clock cycles required are,

CC_T = 2*CC

CC_T = 1200 * 2²²

CC_T = 75 * 2²⁶

Clock speed is 1GH_Z means,

2³⁰ clock cycles = 1 second

75 * 2²⁶ clock cycles, T = (75 * 2²⁶)/2³⁰ seconds

T = 75/2⁴ seconds

T = 4.6875 seconds