Columbia University EE E3910 Elements of Digital Systems

Department of Electrical Engineering Fall 1999

Homework 1

Problem 1.7

Convert the following numbers from the given base to the other three bases listed in the table.

Decimal	Binary	Octal	Hexadecimal
369.3125	?	?	?
?	10111101.101	?	?
?	?	326.5	?
?	?	?	F3C7.A

Problem 1.16

Represent the decimal numbers 831 and 793 in BCD, and then show the steps necessary to form their sum.

Problem 1.21

Show the bit configuration that represents the decimal number 295 in (a) binary, (b) BCD, (c) ASCII, and (d) Unicode.

Problem 2.2

Prove the identity of each of the following Boolean equations, using algebraic manipulation:

(a)

(b)

(c)

(d)

Problem 2.6

Reduce the following Boolean expressions to the indicated number of literals:

(a) to three literals

(b) to two literals

(c) to one literal

(d) to four literals

Problem 2.7

Using DeMorgan’s theorem, express the function

(a) with only OR and complement operations;

(b) with only AND and complement operations.

Problem 2.8

Find the complement of the following expressions:

(a)

(b)

(c)

(d)