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CMSC311 Section 0201 Exam 1
Name
8 March 2001 100 points
(Please print legibly)
The exam has 14 questions worth a total of 100 points. The point value of each question is indicated preceding the question number.
(4) 1. Convert .201 base 3 to decimal. You may leave your answer in fraction form. ii - =7^ .201 base 3 = =?7 - { J decimal
(4) 2. Convert 7.4 decimal to base 3. Round your answer off to three places to the right of the radix point, if necessary.
7.4 decimal = base 3
Z-7 en
(9) 3. Complete the following table for the 4-bit representations (including sign bit). Give your answers in decimal.
Largest number
Most negative number Number of distinct numbers
4-bit Sign Magnitude ~
_-jf
1$
4-bit 1's Complement ^
-"" i
'^ •^ c --S
4-bit 2's Complement ~
~~ <*~^O
/CD
—
(3) 4. Use the 16 bits provided to represent -792 in BCD using 10's complement.
?
ii^o^oo<io// ~ ~r ~~{
' T- ' O
(10) 5. The single precision IEEE 754 standard is as follows:
- 1 sign bit
- 8-bit exponent in excess 127 format
- 23-bit fraction, normalized, with a hidden 1
- Exponents 00000000 and 1 1 1 1 1 1 1 1 are reserved
- 'clean zero' is all zeroes in the exponent and fraction; the sign bit can be 0 or 1
- 'dirty zero' is all zeroes in the exponent, a 0 or 1 in the sign bit, and the magnitude (denormalized) in the fraction with no hidden 1
- Infinity is represented by all ones in the exponent, zeroes in the fraction, and the sign bit 0 or 1
- Not a number (NaN) is represented by all ones in the exponent, the fraction is non zero, and the sign bit is 0 or 1
a. Convert the following decimal values to single precision IEEE 754 format
1.75=£> P2LI-L JJl
.01 5625 = O &/_ j_ i __ __ _ __ __ o ^-^ o o o » o o ooo o DO D o /
b. Convert the following from the IEEE 754 standard to decimal, infinity, or NaN
- 5* S~ = j j oooOOOl 01100000000000000000000
/ -.~<i'( Z =
c. What is the largest gap between consecutive numbers?
d. Excluding clean zeores, dirty zeroes, infinity, and NaN representations, how many ''I/ numbers can be represented?
(8) 8. Show how the 4-to-l MUX below can be used to implement the following function
F(A,B,C) = 2(0,2,3,6)
C — (^) .JX) 01 10 11
/ Ho I
A B
46-) 9. Design a finite state machine (FSM) that reads binary input and creates output of 0 when the input bit matches the previous bit and an output of 1 otherwise.
o
(10) 10. Convert the following to binary, 8-bit representations using 2's complement for negatives. Perform the bit-wise addition. Indicate if overflow occurs. Convert subtraction to addition.
a. 96
Overflow? '
b. 96
1LLQ.OJ1Q
Overflow? /•* °
c. -
_/ / Po^v o o
Overflow? //o
o / / / 'I
(4) 11. Convert the following to binary, 8-bit representation using 1's complement for negatives. Perform the bit-wise addition. Indicate if overflow occurs. Convert subtraction to addition.
96
?'!••? .Pj
/! O O/
O
Overflow?
(10) 12. A serial multiplier operates through a series of shifts and additions. The multiplicand is stored in M and the multiplier in Q. C holds the carry bit from addition. A holds the partial sums. The final answer is in Q and A. If the least significant bit (LSB) in Q is a 1, then M is added to A; otherwise, M is not added. After the LSB of Q is checked, and M is, or is not, added to A, then C, A, Q are shifted to the right. The process is repeated until each bit in Q has been in the rightmost position. Show the results, and whether changes are due to an add or a shift, as the process is implemented with a multiplicand of 0110 and a multiplier of 1010. The initial values are provided. There may be more blank spaces than necessary.
M 0110
C A Q Add or shift? 0 £> c- o O O 0(0f ^r^'
A 0000
<_• ooa
0 1 i o O Q 1 1
O ( I I OQ ^-~\ J, 1 x———-
Q 1010 .0 J 3 i Pi Q i
£> PI 3
L j?o L
loo'
( i oo
_ _^
? O_!_ 1 <? Pi O 1 _ f'K- 1
O _ A • o
y
-i
