You should hand in the solutions to problem 2 and 6 in the tutorial class. Do other problems as well if you can.

- (4.10) [5] What hexadecimal number does this binary number
represent?
1100 1010 1111 1110 1111 1010 1100 1110

- do* (4.1) [25] The Big Picture on page 243 of the textbook
mentions that bits have no inherent meaning. Given the bit pattern
1000 1111 1110 1111 1100 0000 0000 0000

What does it represent, assuming that it is- (a) a two's complement integer?
- (b) an unsigned integer?
- (c) a single precision floating-point number?
- (d) a MIPS instruction?

- (4.21) [10] Find the shortest sequence of MIPS instructions
to determine the absolute value of a two's complement integer.
I. e., convert this instruction (accepted by the MIPS assembler):
abs $10, $11 # $10 = |$11|

This instruction means that register $10 has a copy of register $11 if register $11 is positive, and the two's complement (negatived value) of register $11, if $11 is negative. - (4.28) [5] The full MIPS instruction set has two more
logical operations not mentioned thus far: xor and nor.
The operation xor stands for exclusive OR, and nor
stands for not OR. The table that follows defines these
operations on a bit-by-bit basis.
a b a xor b a nor b 0 0 0 1 0 1 1 0 1 0 1 0 1 1 0 0

Show the minimal MIPS instruction sequence for a new instruction called not that takes the one's complement (invert 0 and 1) of a source register and places it in a destination register. Convert this instruction (accepted by the MIPS assembler).not $10, $20

The not operation in C is the operator `!'. - [15] Write in 6-bit two's complement representation of the integers a=29, b=31, c=-31. (a) Calculate (paper-pencil longhand way) a+b, a-b, b-a, a+c, a-c, and c-a in two's complement arithmetic. Indicate if overflow occurs. (b) Similarly, compute a*b, a*c, b*c, and b/a.
- do* [10] Compute the product of two 5-bit binary numbers,
10101*01011:
- (a) Assuming that the bits represent unsigned values, compute in paper-pencil (longhand) way.
- (b) Follow the steps of third multiplication algorithm.
- (c) Consider the values as two's complement 5-bit numbers, computer by Booth algorithm the paper-pencil (longhand) way.
- (d) Same as (c) but step by step machine way.
- (e) What is the decimal equivalent of the results in (a) to (d) above.