**CSE 370 Solution Set #1
Spring 1999**

1) 0 Points:

Weekly assignments are worth 40% of your final grade. Any
relevant question you'd like to see on the evaluation is fine.

2) 0 Points:

Yes I have an NT account, can login, I'm familiar with the environment
(I should be after 3 years), and I'm subscribed to the mailing list.

3) 4 Points:

a. 2^5+2^4+2^1+2^0 = 51

b. 6*8^1+3*8^0 = 51

c. 3*16^1+3*16^0 = 51

d. 2^6+2^5+2^1+2^-1+2^-3 = 98.625

4) 4 Points:

a. Succesively divide by 2 and look at the remainders.

answer = 11010100 (unsigned binary)

b. Here, since the base is a power of 2, we can group digits. So
each octal digit represents 3 binary digits. 3 = 011 & 7 = 111, so
just concatenate these in the
proper order of significance.

answer = 011111 (unsigned binary)

c. Break the number up into 17 & 0.4375. Convert 17 by
succesively dividing by 2 and looking at the remainders, and convert
0.4375 by succesively
multiplying by 2 and looking at the whole number carries.

answer = 10001.0111 (unsigned binary)

d. Here, since the base is another power of 2, we can group digits.
So each hex digit represents 4 binary digits. D = 1101 & 2 =
0010 & C = 1100 & 3 = 0011,
so just concatenate these again in the proper order of significance.

answer = 1101001011000011 (unsigned binary)

5) 4 Point:

a. 50 (octal)

b. 10010 (unsigned binary)

c. 01011 (unsigned binary)

d. 101011 (unsigned binary)

6) 4 Points:

a. 101111 (signed magnitude binary)

b. 110001 (2s complement binary)

c. In 8-bit 2s complement the smallest number is -128 and the largest
is 127

d. Sign extend the most significant bit = 11111001 (2s complement
binary)

7) 2 Point:

-6 is represented as 1010 in 4-bit 2s complement binary. Assuming
that a 4-bit 2s complement number is written as X4X3X2X1 then this translates to a boolean
expression of X4X3'X2X1'

8) 2 Points:

Here is an example DesignWorks circuit solution.