# ENGR 325

FALL 2015

1. (5) What is 5ED4 07A4 when these values represent unsigned 16-bit hexadecimal numbers? The

result should be written in hexadecimal. Show your work. (P&H 3.1, §3.2)

2. (5) What is 5ED4 07A4 when these values represent signed 16-bit hexadecimal numbers stored in

sign-magnitude format? The result should be written in hexadecimal. Show your work. (P&H 3.2,

§3.2)

3. (5) What is 4365 3412 when these values represent unsigned 12-bit octal numbers? The result

should be written in octal. Show your work. (P&H 3.4, §3.2)

4. (5) What is 4365 3412 when these values represent signed 12-bit octal numbers stored in signmagnitude format? The result should be written in octal. Show your work. (P&H 3.5, §3.2)

5. (5) Assume 185 and 122 are unsigned 8-bit decimal integers. Calculate 185 122. Is there

overflow, underflow, or neither? (P&H 3.6, §3.2)

6. (5) Assume 185 and 122 are signed 8-bit decimal integers stored in sign-magnitude format.

Calculate 185 + 122. Is there overflow, underflow, or neither? (P&H 3.7, §3.2)

7. (5) Assume 185 and 122 are signed 8-bit decimal integers stored in sign-magnitude format.

Calculate 185 122. Is there overflow, underflow, or neither?

8. (5) Assume 151 and 214 are signed 8-bit decimal integers stored in two’s complement format. Calculate 151 + 214 using saturating arithmetic. The result should be written in decimal. Show work

9. (5) Assume 151 and 214 are signed 8-bit decimal integers stored in two’s-complement format.

Calculate 151 214 using saturating arithmetic. The result should be written in decimal. Show

10. (5) Assume 151 and 214 are unsigned 8-bit integers. Calculate 151 + 214 using saturating

arithmetic. The result should be written in decimal. Show your work. (P&H 3.11, §3.2)

11. (5) As discussed in the text, one possible performance enhancement is to do a shift and add instead

of an actual multiplication. Since 9 x 6, for example, can be written (2 x 2 x 2 + 1) x 6, we

can calculate 9 x 6 by shifting 6 to the left three times and then adding 6 to that result. Show the

best way to calculate 0x33 x 0x55 using shifts and adds/subtracts. Assume both inputs are 8-bit

unsigned integers. (P&H 3.17, §3.3)

12. (5) What decimal number does the bit pattern 0x0C000000 represent if it is a two’s complement

integer? An unsigned integer? (P&H 3.20, §3.5)

13. (5) If the bit pattern 0x0C000000 is placed in the Instruction Register, what MIPS instruction will be

executed? (P&H 3.21, §3.5)

14. (5) What decimal number does the bit pattern 0x0C000000 represent if it is a floating point

number? Use the IEEE 754 standard. (P&H 3.22, §3.5)

15. (5) Write down the binary representation of the decimal number 63.25 assuming the IEEE 754 single

precision format. (P&H 3.23, §3.5)

16. Write down the binary representation of the decimal number 63.25 assuming the IEEE 754 double

precision format. (P & H 3.24, 3.5)

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