Data Representation Exercises . Convert 375.375 from decimal to binary with 5 pl

Question

Data Representation Exercises . Convert 375.375 from decimal to binary with 5 places after the binary point. 2. Convert 375.375 from decimal to hexadecimal with 5 places after the hexadecimal point. 3. Convert-1865 from decimal to 16-bit two's complement. 4. Convert-1865 from decimal to 16-bit sign and magnitude. 5. Encode your last name in binary using 1-byte ASCll values for each character 6. Perform the muttiplication problem 137 25 x 2.5 using their binary representations. Verity your final answer. 7. Perform the subtraction problem 40- 43 in 8-bit two's complement 8. Express the RGB color F083A9 (hexadecimal) in decimal values representing the three components separated by commas 9. Using the Huffman Code on page 75, decipher the following Huffman encoding: 111010010010110100100. 10. How many bits would be required to assign a unique bi comprised of 4000 men? Digital Logic Representation: Gates and Circuits Exercises 1. Solve Exercise 56 from Chapter 4. 2. Solve Exercise 60 from Chapter 4 3. Draw a logic circuit diagram for the boolean expression (AB+C) 4. Answer Exercise 64 from Chapter 4. 5. What are the boolean expressions for the outputs of a full adder eircuit (Sum and Carry-out? SSIGNMENT SUBMISSION Text Submission Write Submission Attach File Browse My Computer ADD COMMENTS

Explanation / Answer

Decimal to Binary

Here is an example of using repeated division to convert 1792 decimal to binary:

Decimal to Octal

Here is an example of using repeated division to convert 1792 decimal to octal:

Decimal to Hexadecimal

Here is an example of using repeated division to convert 1792 decimal to hexadecimal:

The only addition to the algorithm when converting from decimal to hexadecimal is that a table must be used to obtain the hexadecimal digit if the remainder is greater than decimal 9.

The addition of letters can make for funny hexadecimal values. For example, 48879 decimal converted to hex is:

Other fun hexadecimal numbers include: AD, BE, FAD, FADE, ADD, BED, BEE, BEAD, DEAF, FEE, ODD, BOD, DEAD, DEED, BABE, CAFE, C0FFEE, FED, FEED, FACE, BAD, F00D, and my initials DAC.

Octal to Binary

Converting from octal to binary is as easy as converting from binary to octal. Simply look up each octal digit to obtain the equivalent group of three binary digits.

Octal to Hexadecimal

When converting from octal to hexadecimal, it is often easier to first convert the octal number into binary and then from binary into hexadecimal. For example, to convert 345 octal into hex:

(from the previous example)

Drop any leading zeros or pad with leading zeros to get groups of four binary digits (bits):
Binary 011100101 = 1110 0101

Then, look up the groups in a table to convert to hexadecimal digits.

Therefore, through a two-step conversion process, octal 345 equals binary 011100101 equals hexadecimal E5.

Octal to Decimal

Converting octal to decimal can be done with repeated division.

The conversion can also be performed in the conventional mathematical way, by showing each digit place as an increasing power of 8.

345 octal = (3 * 82) + (4 * 81) + (5 * 80) = (3 * 64) + (4 * 8) + (5 * 1) = 229 decimal

Decimal Number   Operation   Quotient   Remainder   Binary Result 1792 ÷ 2 = 896 0 0 896 ÷ 2 = 448 0 00 448 ÷ 2 = 224 0 000 224 ÷ 2 = 112 0 0000 112 ÷ 2 = 56 0 00000 56 ÷ 2 = 28 0 000000 28 ÷ 2 = 14 0 0000000 14 ÷ 2 = 7 0 00000000 7 ÷ 2 = 3 1 100000000 3 ÷ 2 = 1 1 1100000000 1 ÷ 2 = 0 1 11100000000 0 done.

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