top-rated free essay

Hexadecimal and Base Conversion Feature

By charly_ Jan 07, 2015 412 Words
﻿
Activity 2.3.1 Hexadecimal and Octal Number Systems

Introduction
We all know that digital electronics use the binary number system. However, with new computers containing 32, 64, and even 128 bit data busses, displaying numbers in binary is quite cumbersome. For example, a single piece of data on a 64-bit data bus would look like this:

0110100101110001001101001100101001101001011100010011010011001010

Obviously, presenting data in this form would invite error. For this reason we use the hexadecimal (base 16) and, to a lesser extent, the octal (base 8) number systems. In this activity you will learn how to convert numbers between the decimal, binary, octal, and hexadecimal number systems.

Equipment
Calculator (preferably one with a number base conversion feature) Circuit Design Software (CDS)

Procedure
Complete the following decimal-to-octal number conversions. If available, use the base conversion feature of your calculator to check your answers. 1) 25 (10) = 11 (8)
2) 49 (10) = 11 (8)
3) 187 (10) = 73 (8)
4) 398 (10) = 616 (8)
5) 2879 (10) = 5477(8)

Complete the following octal-to-decimal number conversions. If available, use the base conversion feature of your calculator to check your answers. 6) 36 (8) = 30 (10)
7) 75 (8) = 61 (10)
8) 143 (8) = 49 (10)
9) 367 (8) = 247 (10)
10) 1735 (8) = 989 (10)

Complete the following decimal-to-hexadecimal number conversions. If available, use the base conversion feature of your calculator to check your answers. 11) 25 (10) = 19 (16)
12) 46 (10) = E2 (16)
13) 120 (10) = 78 (16)
14) 429 (10) = 1AD (16)
15) 1215 (10) = B4F (16)

Complete the following hexadecimal-to-decimal number conversions. If available, use the base conversion feature of your calculator to check your answers. 16) 3B (16) = 59 (10)
17) A9 (16) = 169 (10)
18) 159 (16) = 345 (10)
19) 2A3 (16) = 675 (10)
20) 1AB3 (16) = 6835 (10)
Utilize the shortcut base conversion technique to complete the following table.

Binary
Octal
1)
1010112
53
2B
2)
110100011
643
1A316
3)
110101102
326
D61
4)
1011111
1378
5F
5)
1010111102
536
15E

A useful tool in simulation is the Digital Hex Display. Create the following circuit in the Circuit Design Software (CDS) and complete the truth table.

The HEX DISPLAY has a built-in decoder that converts a binary number into its corresponding display digit. For example an input of ‘0110’ would display a ‘6’, and a ‘1010’ would display an ‘A’.

Conclusion
1. Without performing the conversion, which of the following numbers is the octal equivalent of 24510? How were you able to determine this? a. 3798
b. 1748
c. 3658
2. You are sent to the store to buy some hamburger for dinner. When you come home, your sister looks at the UPC label on the meat and says, “We can’t use this.” What does she see on the label that you do not? Hint: think hexadecimal.

Going Further – Optional
1. With 128-bit graphic cards becoming standard on many new PCs, there has been some thought of expanding to the base 32 number system. The base 32 number system would be selected because it is the next greatest power of two after 16. Use your knowledge of number systems to convert the following base 32 number into its decimal equivalent.

4P8M (32) = ____________ (10)

Related Documents

• Conversion between Number Bases

...4.3 4.3 Conversion Between Number Bases 169 Conversion Between Number Bases Although the numeration systems discussed in the opening section were all base ten, other bases have occurred historically. For example, the ancient Babylonians used 60 as their base. The Mayan Indians of Central America and Mexico used 20. In this sectio...

• Number Conversion

...COUT 4-BIT ADDER Ci 0 C3 C2 C1 C0 Ovidiu Ghita Page 89 Digital Electronics, 2003 OCTAL & HEXADECIMAL NUMBERS TWO MORE NUMBER SYSTEMS OCTAL >>> BASE 8 E.G. 38 HEXADECIMAL >>> BASE 16 E.G. 516 THE OCTAL NUMBER SYSTEM COMPOSED OF 8 DIGITS: 0, 1, 2, 3, 4, 5, 6, 7 IS TO COUNT ABOVE 7, WE BEGIN ANOTHER COLUMN AND START OV...

• Number Conversions

...This is also shown in the following example. Weights = 128 64 32 16 8 4 2 1 Bits = 0 1 1 1 1 1 0 1 64 + 32 + 16 + 8 + 4 + 1 = 125 Task 2: Procedure 1.Convert the binary number 10101101 into decimal. Use the method of adding weights as shown in the example from Task 1. Weights = 128 64 32 16 8 4 2 1 Bits = 1 0 1 0 1 1 0 1 128 + 32 + ...

• Conversion of Number Systems

...THE PROJECT ON CONVERSION OF NUMBER SYSTEMS INDEX Sr no. | TOPIC | Pg No | 1. | Title | 1 | 2. | Subtitle | 1 | 3. | Abstract | 2 | 4. | Introduction | 3 | | 4.1 | Decimal System | 5 | | 4.2 | Binary Syste...

• Assignment: Hexadecimal and Following Decimal Numbers

... Due Date: 11-03-2013 Section V and V3 1. List the first 16 numbers in base 12. Use the alphabets A and B for the last two digits. (4) Base 10 | Base 12 | 0 | 0 | 1 | 1 | 2 | 2 | 3 | 3 | 4 | 4 | 5 | 5 | 6 | 6 | 7 | 7 | 8 | 8 | 9 | 9 | Last...

• Base

...New Military Base There are many types of military bases; some have piers for ships and submarines, others have air strips for planes and others provide training for military members. A new military installation can provide employment opportunities for community members. A military base can increase the revenue generated by local businesse...

• Base

...Leader's Book Notes - Boots June 20, 2008 By SMA Kenneth Preston Leaders Book Note - Boots   Leaders,  In this edition of my leader book notes I would like to inform leaders of the authorized and unauthorized Commercial-Of-The-Shelf (COTS) and Army issued boots for wear with the ACUs.    There has been misunderstanding wi...

• Feature

...still very bizarre. The Takagism series are all very classic puzzle games, ever since the developer came up with the first edition called ‘Crimson Room’; the game soon gained popularity among the players around the world. Now, you can experience all these by yourselves, in many cities, conspiracy rooms like Takagism provide different ...