Question

a)Given a 100M line program with the following cycle breakdowns: 50% R-type 25% load-store 25% branch. How long would it take to execute on a single cycle processor running at 1MHz

b)How long would it take to execute on a pipleine processor running at 10MHz, where: 50% of R type instructions incur a 1 cycle stall 50% of load-store incur a 3 cycle stall all branches incur a 1 cycle stall.

Answer 1

a) Given a 100M line program with the following cycle breakdowns: 50% R-type 25% load-store 25% branch. How long would it take to execute on a single cycle processor running at 1MHz

Given:

Total lines in program = 100 x 10⁶

Assume CPI ie clocks per instruction = 1

Total cycles required for program to execute = 100 x 10⁶

For the Given single cycle processor:

Frequency = 1MHz = 10⁶ Hz

So,

Time required to execute whole program = total cycles required / frequency = 100 x 10⁶ / 10⁶ = 100 seconds

b)  How long would it take to execute on a pipeline processor running at 10MHz, where: 50% of R type instructions incur a 1 cycle stall 50% of load-store incur a 3 cycle stall all branches incur a 1 cycle stall.

New frequency = 10 MHz = 10 x 10⁶

From previous part,

Total cycles required for program to execute = 100 x 10⁶

50% are R-type, 25% are load-store, 25% are branch.

R_c = R- type instruction count = 50% = 50 x 10⁶

_LSc = load-store instruction count = 25% = 25 x 10⁶

B_c = branch instruction count = 25% = 25 x 10⁶

Assume CPI for simple instructions = 1

50% of R-type instructions incur a 1 cycle stall

CPI_R = Average CPI for R-type instructions = .5( 1) + .5( 1+1 ) = 1.5

50% of load-store instructions incur 3 cycle stall

CPI_LS = Average CPI for load-store instructions = .5(1) + .5( 1+3 ) = 2.5

all branch instructions incur a 1 cycle stall

CPI_B = Average CPI for branch instructions = 1+1 = 2

T_c = Total cycles required to execute whole program = R_c x CPI_R + LS_c x CPI_LS + B_c x CPI_B

=> T_c = 1.5 x R_c + 2.5 x LS_c + 2 x B_c = 1.5 x 50 x 10⁶ + 2.5 x 25 x 10⁶ + 2 x 25 x 10⁶

=> T_c = 75 x 10⁶ + 62.5 x 10⁶ + 50 x 10⁶ = 187.5 x 10⁶

So,

Time required to execute whole program = total cycles required / frequency = 187.5 x 10⁶ / 10 x 10⁶ = 18.75 seconds

//do comment if any problem arises