Homework 11
Reading assignment:
- Peterson & Weldon,
"Error-Correcting Codes," MIT Press, (Second Edition), (1986), Chapter 7.
- Gill, "Linear Sequential
Circuits," McGraw-Hill, (1966), Chapter 2.
Problem 1.
- (a) Draw the linear
sequential circuit (LSC) that multiplies by the polynomial
h(x)
= 1 + x3 +x6
- (b) Draw the linear
sequential circuit (LSC) that divides by the polynomial
g(x) = 1 + x2
+ x4 + x6 + x7
- (c) Draw the linear
sequential circuit (LSC) that simultaneously multiplies by
h(x) and
divides by g(x).
Problem 2.
Draw an LSC which takes as inputs polynomials
a(x) and
b(x) and then
produces the output h(x)a(x) + k(x)b(x),
where h(x)
and k(x)
are the polynomials:
h(x) = 1 + x4 + x10
and k(x) = x + x2 + x4
+ x7 + x9