A computer has a branch target buffer, BTB. Derive an expression for the average branch penalty if the following apply. 

• A branch not in the BTB that is not taken incurs a penalty of O cycles. 

• A branch not in the BTB that is taken incurs a penalty of 6 cycles. 

• A branch in the BTB that is not taken incurs a penalty of 4 cycles. 

• A branch in the BTB that is taken incurs a penalty of O cycles. 

• The probability that a branch instruction is cached in the BTB is 80%. 

• The probability that an instruction not in the BTB is taken is 20%. 

• The probability that an instruction in the BTB is taken is 90%.