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4 problems, 3 pages Exam Two Solution 22 March 2000
Problem 1 (3 parts, 30 points) Implementing Storage
For each part of this problem, connect the inputs and output of your design to the named signals.
Part A (10 points) Using only the devices below, implement a two-to-one mux.
Part B (10 points) Now using this two-to-one mux, implement a transparent latch using basic gates (NAND, NOR, AND, OR, NOT, pass). Try to minimize transistors.
Part C (10 points) Now using a two-to-one mux and two transparent latches, implement a register with read and write enable using basic gates (NAND, NOR, AND, OR, NOT, pass).
4 problems, 3 pages Exam Two Solution 22 March 2000
Problem 2 (3 parts, 30 points) Numbers and Arithmetic
Part A (9 points) Convert some binary values (and powers of two) into decimal notation:
binary notation decimal notation
1111.111 15.
110001010 394
247 128 Trillion
Part B (9 points) Convert the following octal values into hexadecimal notation:
octal notation hexadecimal notation
101 41
7734 FDC
156.17 6E.3C
Part C (12 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 no yes no
unsigned error?
yes yes no no
4 problems, 3 pages Exam Two Solution 22 March 2000
Problem 4 (2 parts, 20 points) Priority Fun
Consider a priority encoder with the following behavior:
In3 In2 In 1
In 0 O 1 O 0 Valid
0 0 0 0 X X 0
X 0 0 1 0 0 1
X X 1 X 0 1 1
X 1 0 X 1 0 1
Part A (10 points) List the inputs (In 0 , In 1 , In 2 , and In 3 ) in increasing priority.
IN 3 < IN 0 < IN 2 < IN 1
lowest priority 3 rd^ highest priority 2 nd^ highest priority highest priority
Part B (10 points) The behavior of O 1 is summarized below (in map format). Derive a simplified sum of products expression using a Karnaugh Map. Circle and list the prime implicants, indicating which are essential. Then write the simplified SOP expression.
O 1 = (^) In 1 ⋅( In 0 + In 2 )
