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4 problems, 6 pages Exam Two 22 March 2001
Problem 1 (6 parts, 35 points) Numbers and Arithmetic
Part A (6 points) Convert these binary values (and powers of two) into decimal notation:
binary notation decimal notation
11001100.101 204.
11100111 231
215 35 Thousand
Part B (6 points) Convert the following octal values into hexadecimal notation:
octal notation hexadecimal notation 236 010011110 = 9E
771177 111111001001111111 = 3F27F
52.25 101010.010101 = 2A.
Part C (9 points) For each problem below, (a) compute the operations using the rules of addition, (b) indicate whether an error occurs assuming all numbers are expressed using a four bit two’s complement representation, and (c) indicate whether an error occurs assuming all numbers are expressed using a four bit unsigned representation.
addition result
signed error?
no yes no
unsigned error?
yes no no
4 problems, 6 pages Exam Two 22 March 2001
Part D (6 points) For each problem below, (a) compute the operations by negating and adding the lower number, (b) indicate whether an error occurs assuming all numbers are expressed using a four bit two’s complement representation, and (c) indicate whether an error occurs assuming all numbers are expressed using a four bit unsigned representation.
- 1 1 0 0 subtraction result
signed error?
yes no
unsigned error?
yes yes
Part E (4 points) What is the minimum number of bits needed to represent the following decimal integers in an unsigned integer representation?
a) 45,387: 16 bits.
b) 32: 6 bits.
Part F (4 points) What is the minimum number of bits needed to represent the following decimal integers in a signed two’s complement integer representation?
a) 45,387: 17 bits.
b) -19: 6 bits.
4 problems, 6 pages Exam Two 22 March 2001
Problem 3 (3 parts, 20 points) Building Blocks
Consider a priority encoder with the following behavior:
In 2 In 1 In 0 O 1 O 0 Valid 0 0 0 X X 0 0 0 1 0 0 1 0 1 0 0 1 1 0 1 1 0 1 1 1 0 0 1 0 1 1 0 1 0 0 1 1 1 0 0 1 1 1 1 1 0 1 1
Part A (6 points) List the inputs (In 0 , In 1 , In 2 , and In 3 ) in increasing priority.
In 2 < In 0 < In 1 lowest priority 2 nd^ highest priority highest priority Part B (10 points) Design a 4-to-1 multiplexor using only pass gates and inverters. Clearly label all inputs and outputs. How many transistors are in your implementation? S 0
I 0
I 1
S 1
I 2
I 3
Out
Number of transistors: 16.
Part C (4 points) Design a 1-to-4 demultiplexor using the 4-to-1 mux you designed in part B (in icon form). Clearly label the inputs and outputs.
I 0
I 1
I 2
I 3
S 1
Out 4-to- MUX
S 0
In
O^0
O 1
O 2
O 3
S 0 S^1
4 problems, 6 pages Exam Two 22 March 2001
Problem 4 (1 part, 15 points) Registers and Timing
Consider the register implemented below.
In Out
En
Latch
In Out
En
Latch
mux
out
IN^ s
WE
OUT
A
phi1 phi
Assume the following signals are applied to your register. Draw the signal at point A (output of the first latch) and the output signal Out. Assume A and Out start at zero.
In
WE
Out
A
