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When a program is run on Computer X, 50% of the execution time is CPU time . A better Computer Y reduces the execution time by 20%. It is know that Computer Y has a clock rate of 2 GHz, and it takes Computer Y 10% more clock cycles to execute the program. In addition, Computer Y can only reduce CPU time. What is the clock rate in GHz of Computer X? The answer must have exactly one digit after the decimal point, even if it is zero, e.G. 2.0 or 0.9. 

[Clock Rate Y - (Clock Rate Y)(Clock Cycle % Y)] - [Clock Rate Y - (Clock Rate Y)(Clock Cycle % Y)][Computer Y Reduction Time]

2GHz - (2GHz)(10%) = 1.8GHz

1.8GHz - 1.8GHz(20%) = 1.44GHz

Answer: 1.4GHz



When converting a base-N fractional number 0.A1a2...An-1an to decimal, the formula of a1×N-1 + a2×N-2 + ... + an-1×N-(n-1) + an×N-n is used. Given a base-2 number 0.11001111111, what is the value of am×N-m for m being 5? If the answer has more than 15 digits after the decimal point, round and keep only 15 digits after the decimal point.

  1. Digit = Count m digits from the right of the base-x integer starting with 0

0.110011111115

  1. =1 / [Digit*(base number integer) ^ m]

=1 / 1(2)^5

=1/ 32

=0.03125

Answer: 0.03125


When converting the decimal integer 112 to base-2 using the subtraction method, a number of non-zero integers will be subtracted from the integer to be converted. Show those integers from large to small, separated by comma.


112 - 26= 4826 = 64

48 - 25= 1625 = 32

16 - 24= 024 = 16



Given a 9-bit binary sequence 110111010, show the decimal integer it represents in sign magnitude, one's complement, two's complement and excess-255 respectively in the given order, separated by comma.



First three answers will be negative and the excess will be positive

Sign Magnitude: Take 1 at the beginning off the binary number and convert to decimal and make it negative

1 10111010 = 10111010

  2 + 8 + 16 + 32 + 128 = -186

One’s Complement:Take sign-magnitude binary number, set the 1 at the beginning aside and switch the numbers (1 = 0, 0 = 1)

110111010 = 01000101

  1 + 4 +64 = -69

Two’s Complement: Subtract 1 from one’s complement

-69 - 1 = -70

Excess-Number: Convert the whole binary number including the 1 at the beginning, subtract the excess from that number.

110111010 = 442

442 - 255 = 187

Answer: -186, -69, -70, 187Answer: 64,32,16


Given a 9-bit binary sequence 011000101, show the decimal integer it represents in sign magnitude, one's complement, two's complement and excess-255 respectively in the given order, separated by comma.

Sign Magnitude: Convert binary to decimal

011000101 = 1 + 4 + 64 + 128 = 197

One’s Complementand Two’s Complement: Same as 

Excess-X: Subtract the excess number from the sign magnitude 

197 - 255 = -58

Show the decimal integer -134 in 9-bit sign magnitude, one's complement, two's complement and excess-255 respectively in the given order, separated by comma.

Sign Magnitude: Convert the 134 to binary and add a 1 at the beginning

10000110 = 110000110

One’s Complement: Take sign-magnitude binary number, set the 1 at the beginning aside and switch the numbers (1 = 0, 0 = 1)

1 10000110= 1 01111001

Two’s Complement: Take one’s complement and add 1

101111001 + 1 = 101111010

Excess-Notation: Excess number - positive decimal integer = answer in binary

255 - 134 = 121

121 to binary = 001111001

Answer: 110000110, 101111001, 101111010, 001111001


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