Introduction To Binary Codes printable pdf download

Introduction To Binary Codes

ECE 204 - BINARY NUMBERS AND CODES - INV 11

INTRODUCTION TO BINARY CODES

FALL 2003

A.P. FELZER

To do "well" on this investigation you must not only get the right answers but must also do neat,

complete and concise writeups that make obvious what each problem is, how you're solving the

problem and what your answer is. You also need to include drawings of all circuits as well as

appropriate graphs and tables.

From the last three Investigations we know how to convert numbers from decimal to binary and

back again to decimal. And we know how to use 2's complement arithmetic to add and subtract

positive and negative numbers. The objective of this Investigation is to introduce some other codes

including octal, hex and BCD codes for representing numbers and Gray codes for representing

physical locations.

1. We begin with some review problems

a. Convert 87 to 8-bit binary

b. Convert –87 to 8-bit signed magnitude

c. Convert –87 to a 10 bit 2's complement number

d. Calculate the following sum of 2's complement numbers: A = 10110

+ 01101

e. Calculate the following difference of 2's complement numbers: B = 11101

– 00101

2. Binary numbers like the following

10110101100101011

are of course great, but keeping track of them is in general tedious and prone to error. One way

to reduce this problem is to write our binary numbers in hexadecimal (hex) which is base

16. The objective of this and the next problem is to introduce the hex number system with the

following sixteen symbols

Hex

Decimal

0–9

and place values equal to

. . . 16

Memorize these results and then

a. Convert B3

to decimal

b. Convert 2D

to decimal

c. Convert 2A7

to decimal

3. What makes hex numbers so nice is that they're easy to convert back and forth to binary as

illustrated in the following example

Introduction To Binary Codes