**ENEE
244 (01**). Spring 2006 **

**
Homework 2**

*Due back in class on Monday, Feb
27.*

**1**. Represent the number 7429
in BCD code.

**2**. Convert the BCD number 00110101 to decimal.

**3**. State one advantage of the 2421 code over the
regular (8421) BCD code.

**4**. A transmitter using an even-parity scheme
transmits the byte 01011011.

(a) What is the parity bit that is transmitted?

(b) Suppose during transmission only the parity bit is erroneously flipped because of interference. Is this error detected at the receiver?

**5.** How many distinct
double-bit errors can occur in a 7-bit ASCII character? How many of these errors
change the character's parity? How many are detected?

**6**. Determine whether the *nor*
operator ~ defined by a~b = (a+b)' is associative, commutative, or distributive
over +*.*

**7**. We know that ac'.1 = ac'. Write the dual of this
equation.

**8**. Simplify the 3-input boolean
function Σ m(1,2,6,7) in terms of the inputs x, y and z.

**9**. Express the 3-input
boolean function Σ m(2,3,4,6) in maxterm canonical form.

**10**. Use algebraic techniques to determine
whether or not the following Boolean equation is valid:

(abd + a'b + b'd + c')(c + ab + bd) =?
b(a+c)(a'+c') + d(b+c)