Representing Digital Data 26-38

Why is the answer 48?

Bits Provided to the Mathematical Engine: 0001 0000 0000 0010 0000 0011 The first byte is 0001 0000 which represents the number 16. The second byte 0000 0010 represents the mathematical operation which is defined as multiplication. The third byte is 0000 0011 which represents the number 3. The mathematical engine would use this information to multiply 16 by 3 and it would return a result of 48.

How would the binary number 1001 1111 1011 0010 be represented in hexadecimal format? A. 9EA2 B. 5FB1 C. 9FB2 D. 9FA2

C. 9FB2

A programmer developed a mathematical engine that could perform basic mathematical calculations. The engine required that it be given exactly three consecutive bytes of information. The first byte would signify an integer. The second byte would indicate the mathematical operation, and the third byte would be another integer. For example, to divide 12 by 3, the first byte would represent the number 12, the second byte would signify division, and the third byte would represent the number 3. The engine would return the result in decimal format. The second byte could have the following values: 0000 0000 = addition 0000 0001 = subtraction 0000 0010 = multiplication 0000 0011 = division What would this mathematical engine return if it were given the following stream of bits? 0001 0000 0000 0010 0000 0011 A. 48 B. 32 C. 13 D. 19

A. 48

The ASCII (American Standard Code for Information Interchange) is a character encoding scheme that translates characters into numbers and can be used with either decimal or hexadecimal numbers. A portion of the table, with decimal numbers, follows: Decimal Character 65 A 66 B 67 C ... ... 97 a 98 b 99 c ... ... Take the hexadecimal code for CPU. Add to that number 2f 11 18. Then convert the result using the ASCII table. What is the result? A. ram B. aol C. lol D. cat

A. ram

Why is ram the correct ASCII result?

Start with figuring out where in the alphabet the letters are: CPU: 3rd, 16th, 21st. A is 65, so we will need to add 2, 15, and 20 to 65: add 2 add 15 add 20 65+ 2 = 67 65 + 15 = 80 65 + 20 = 85 Before you can add the numbers, you must convert these numbers to base 16 (hexadecimal). To do this, divide by 16 and keep the remainder for each division: divide by 16 divide by 16 divide by 16 67 / 16 = 4R3 80/16= 5RO 85/16= 5R5 Next, take these three numbers in hexadecimal and add the numbers you were given: add 2f add 11 add 18 43+2f+72 50+11=61 55+18+6d Then these must be converted back to the letters: ram

Why is it machine 2, machine 4, and machine 5?

The status of 52 is a decimal number which will need to be converted into binary in order to see the sequence of bits which represent each machine's status. We are told that there are 8 machines numbered from 0-7, so there are a total, of 8 bits. To convert to binary, subtract the largest power of two that is not greater than the number. Use that answer and again subtract the largest power of 2. Keep repeating until zero is reached. 52-32= 20 20-16=4 4-4=0 When writing the binary each power of 2 that was subtracted represents a 1 and the powers of 2 that were not subtracted represent a 0. Arrange these 11s and 0s to form the binary number. Using this binary sequence, it is clear that machines 2, 4, and 5 are in service since their bit values are 1.

Why do hexadecimal representations use fewer digits than binary values and make it easier to express values?

A color can be expressed using 6 digits under the #RRGGBB hexadecimal color coding. To represent the same value in binary, 24 digits would be needed.

When a person wants to refer to a specific color, he/she may describe it by its red, green, and blue (RGB) value or by its hexcode. The RGB values are decimal numbers separated by commas, and the hexcode is the 2-digit hexadecimal equivalent of each of the red, green, and blue values. For example, the RGB value for the color "army green" is (75, 83, 32) and its corresponding hexcode is #4b5320. Note that 4b, 53, and 20 are the hexadecimal equivalents for the decimal numbers 75, 83, and 32 respectively. If the RGB value for a color is (21, 60, 46), what is the color's hexcode? A. #153c2e B. #152b2d C. #163d2f D. #216046

A. #153c2e

Why is B the correct answer choice?

As seen in the previous question, the number of colors that can be represented using the #RRGGBB format is 16^6. . The total number of colors that can be represented using the #RGB format is 16⋅16⋅16= 16^3 ⋅ The number of colors that are lost or cannot be represented by this simplified format is the difference between the respective total number of colors. Total number of colors in #RRGGBB) - (Total number of colors in #RGB) = 16^6 -16^3

Computer systems use binary numbers to represent data that it processes. If it has a number in memory represented by the binary number 0010 1001, and it is processing an instruction to add the decimal number 21 to it, what is the resulting number in binary format? A. 0110 1011 B. 0011 1001 C. 0110 0110 D. 0011 1011

B. 0011 1001

One way of communicating hexadecimal color codes is in the following way: #RRGGBB. The first pair of numbers represents the red color value (R), the second pair represents the green color value (G), and the third pair represents the blue color value (B). Sometime a simplified color code scheme is used that follows this format: #RGB. In this format, only the first digits of each color component from the original format are used (#RRGGBB). How many fewer colors are represented using this color code scheme (#RGB) as compared to the original format (#RRGGBB)? A. 16^3 B. 16^6-16^3 C. 1/2(16^6) D. 8^6

B. 16^6-16^3

Why are A,B, and C not the answer?

The 4 possible combinations are: 10001119 91000111 471001 100147 D or 100147 is the only possible combination in the answer choices.

he ASCII (American Standard Code for Information Interchange) is a character encoding scheme that translates characters into numbers and can be used with either decimal or hexadecimal numbers. A portion of the table, with the decimal number, follows: 65 A 66 B 67 C ... ... 97 a 98 b 99 c ... ... Using the information above, translate the following characters into their hexadecimal equivalent: A. 6a 70 65 67 B. 4a 50 45 47 C. 4a 70 65 67 D. 74 80 69 71

B. 4a 50 45 47

A metal fabricating company owns a variety of machines that are used to cut and shape metal products. The company stores the status of each of its eight machines as a sequence of bits. A bit value of 1 means that the machine is in service and a bit value of 0 means that the machine is out of service. Each machine is given a number from 0-7 (machine 0, machine 1, ..., machine 7). The status of machine 0 is represented by the rightmost bit, machine 1's status is represented by the bit left of the rightmost bit, and machine 7's status is represented by the leftmost bit, etc. The company communicates the status of its machines to its supervisors by using the decimal equivalent of these series of bits. If the company communicates its machine statuses as the decimal number 52, which machines are currently in service? A. Machine 0, 4, 5, and 7 B. Machine 2, 4, and 5 C. Machine 1, 3, and 4 D. Machine 0, 1, 3, 6, and 7

B. Machine 2, Machine 4, Machine 5

The following image shows four different representations of data? R: 127 G: 79 B: 201 Purple #7F4FC9 0111 1111 0100 1111 1100 1001 All of the following show an ordering of representations from lower levels of abstractions to higher levels of abstractions except: A. binary --> ASCII B. hexadecimal --> color C. color --> binary D. binary --> color

C. color --> binary

Why are A, C, and D incorrect?

Choice 'A' is incorrect, as it converts to jpeg, all lower case. Choice 'B' is incorrect, as it converts to Jpeg, with only the first letter upper case. Choice 'D' is incorrect, as it converts to JPEG, but is in decimal, not hexadecimal.

Why are A, B, and D wrong?

Choice 'A' is incorrect. 9EA2 in hexadecimal is equivalent to 1001 1110 1010 0010 in binary format. Choice 'B' is incorrect. 5FB1 in hexadecimal is equivalent to 0101 1111 1011 0001 in binary format. Choice "D" is incorrect. 9FA2 om hexadecimal is equivalent to 1001 1111 1010 0010 in binary form.

Why are A,B, and D incorrect?

Choice 'A' is incorrect. ASCII is a higher level of abstraction than binary in the sense that a multiples bits arte reduced to fewer ASCII characters. The details of the 1's and 0's of binary are not the focus. Choice 'B' is incorrect. Color is a higher level of abstraction than hexadecimal in the sense that a pixel (for the color) represents several hexadecimal digits. Choice 'D' is incorrect. Color is a higher level of abstraction than binary in the sense that multiple bits are reduced to a single pixel (for the color).

Why are A, B, and C incorrect?

Choice 'A' is incorrect. Binary, not hexadecimal, representation of data is at the lowest level of abstraction. Choice 'B' is incorrect. Numbers can be converted from any base to any other base in a simple fashion. Pixel data can be directly converted to hexadecimal or binary, and converting to binary is no more difficult than converting to hexadecimal. Choice "C" is incorrect. The 16 digits for hexadecimal allow it to represent values in a shorter more compact manner. However, the same values can be represented with binary's 2 digits in a longer form.

Why is that a potential code for unlocking the door?

The decimal number 71 is equivalent to 1000111 in binary format and 47 in hexadecimal format. The number 9 in equivalent to 1001 in binary and 9 in hexadecimal format. Since it is unknown which order the numbers are in and which is converted to binary format and which is converted to hexadecimal format, there are four possible combinations. Of these four combinations, the only one listed on the answer choices is 100147.

Why did Contestants A, C, and D not win?

Choice 'A' is incorrect. Contestant A had a vote tally of 11001. The total "thumbs up" votes for the live and online audiences is 2, and since only one judge gave a "thumbs up", the weighted judge vote is (2)(1) = 2. The total weighted vote count is 2+2= . This is lower than Contestant D's weighted vote count of 6. Choice 'B' is incorrect. Contestant B had a vote tally of 10110. The total "thumbs up" votes for the live and online audiences is 1, and since two judges gave a "thumbs up", the weighted judge vote is (2)(1)=2. The total weighted vote count is 1+4=5. This is lower than Contestant D's weighted vote count of 6. Choice 'C' is incorrect. Contestant C had a vote tally of 01101. The total "thumbs up" votes for the live and online audiences is 1, and since two judge gave a "thumbs up", the weighted judge vote is (2)(2) = 4. The total weighted vote count is 1+4=5. This is lower than Contestant D's weight count vote of 6.

Why is the answer not A, C, or D?

Choice 'A' is incorrect. If Machines 0, 4, 5, and 7 are in service, this would be represented by the binary sequence 1011 0001. This binary number is equivalent to (1)(128)+(0)(64)+(1)(32)+(1)(16)+(0)(8)+(0)(4)+(0)(2)+(1)(1)= 128+32+16+1=177 in decimal. Choice "C" is incorrect. If machines 1,3,, and 4 are in service, this would be represented by the binary sequence 0001 1010.sequence.This binary number is equivalent to (0)(128) + (0)(64) + (0)(32) + (1)(16) + (1)(8) + (0)(4) + (1)(2) + (0)(1) = 16 + 8 + 2 = 26 in decimal. Choice 'D' is incorrect. Note that the decimal number 52 is equivalent to the binary number 0011 0100. Machines 0, 1, 3, 6, and 7 are actually the machines that are out of service, not in service, since their corresponding bit values are 0.

Why are the answer choices A, B, and C incorrect?

Choice 'A' is incorrect. This choice is equivalent to 256, which is the total number of values that a single component can take on. For example, there are 256 different brightnesses/intensities for red. Choice 'B' is incorrect. This choice considers 16 values for each color component (R's, G's, B's) and computes the following combination: 16x16x16= 16^3 . Choice 'C' is incorrect. This choice was most likely selected out of guessing.

Why are A, C, and D incorrect answer choices?

Choice 'A' is incorrect. This is the total number of colors that can be represented in the #RGB format. 16⋅16⋅16= 16^3 Choice 'C' is incorrect. This choice is equivalent to half of the original number of colors represented under the #RRGGBB format. This is misleading since the total number of digits in the format are cut in half. Due to the nature of the hexadecimal format, taking away half of the digits results in much more than half of the color possibilities being lost. Choice 'D' is incorrect. This choice is the incorrect simplification of Choice 'C'. The 1/2 was multiplied with the base number of 16 so 1/2(16^6) became 8^6.This is not mathematically correct.

Why are B, C, and D incorrect?

Choice 'B' is incorrect. A result of 32 would be correct if the last byte were 0000 0010 (which represents 2), since 16 x 2 = 32. Choice 'C' is incorrect. A result of 13 would be correct if the middle byte were 0000 0001 (indicating subtraction), since 16 - 3 = 13. Choice 'D' is incorrect. A result of 19 would be correct if the middle byte were 0000 0000 (indicating addition), since 16+3+19.

Why are B, C, and D incorrect answer choices?

Choice 'B' is incorrect. The hexcode #153b2d is equivalent to the RGB value (21, 59, 45). Choice 'C' is incorrect. The hexcode #163d2f is equivalent to the RGB value (22, 61, 47). Choice 'D' is incorrect. The hexcode #216046 is equivalent to the RGB value (33, 96, 70).

Why is the resulting number 0011 1001?

Choice 'B' is the correct answer. The binary number 0010 1001 is equivalent to the decimal number 41, since (1)(2^5)+(0)(2^4)+(1)(2^3)+(0)(2^2)+(1)(2^1)+(1)(2^0) = 32+8+1=41. When the computer adds the decimal numbers 21 and 41, the result is 62 in decimal format. Since, the result is 62 in decimal format. Since the choices are all expressed in binary format, the decimal number 62 needs to be converted to binary format. To convert to binary, subtract the largest power of 2. Keep repeating until zero is reached. The answer is 0011 1110. The rest of the binary answer choices are not the equivalent to the decimal number 62.

Why is color --> binary not in order from lower levels to higher levels?

Color --> binary goes from a higher level of abstraction to the lowest level of abstraction. Remember, all digital data can be represented by binary(bits).

An escape room was designed so that the last puzzle to solve in order to exit the room was determining the code to unlock the door. The participants found the following sequence of numbers taped on the back of a picture: 71, 9 and a separate clue which indicated that these two numbers are in decimal format and may not be in the correct sequence. However, the door's lock requires a combination of one of these two numbers in binary format and the other number in hexadecimal format, These two converted numbers would be entered one after the other to open the door. Which of the following is a potential for unlocking the door? A. 10001118 B. 91000110 C. 461010 D. 100147

D. 100147

Hexadecimal color codes are communicated in the following way: #RRGGBB. The first pair of numbers represents the red color value (R), the second pair represents the green color value (G), and the third pair represents the blue color value (B). How many colors can be represented using this color code scheme (#RRGGBB)? A. 16^2 B. 16^3 C. 16^4 D. 16^6

D. 16^6

A television show features contestants with a variety of different talents. After the contestants highlight their talents, each of the three judges gives either a "thumbs up" or a "thumbs down". The live audience also votes and if a majority votes as "thumbs up", then the overall audience vote is a "thumbs up". Else, the overall audience vote is a "thumbs down". Online voting works in the same fashion. A television show features contestants with a variety of different talents. After the contestants highlight their talents, each of the three judges gives either a "thumbs up" or a "thumbs down". The live audience also votes and if a majority votes as "thumbs up", then the overall audience vote is a "thumbs up". Else, the overall audience vote is a "thumbs down". Online voting works in the same fashion. The following are the final voting results for the four contestants. Contestant A: 11001 Contestant B: 10110 Contestant C: 01101 Contestant D: 00111 Which contestant won the competition? A. Contestant A B. Contestant B C. Contestant C D. Contestant D

D. Contestant D

Hexadecimal color codes are communicated in the following way: #RRGGBB. The first pair of numbers represents the red color value (R), the second pair represents the green color value (G), and the third pair represents the blue color value (B). Which statement correctly captures why hexadecimal values are more commonly used to represent colors as compared to binary values? A. Hexadecimal represents data at the lowest level of abstraction B. It takes to much work to convert pixels (colors) to binary C. Hexadecimal can represent more colors because it has 16 digits as compared to binary's 2 digits D. Hexadecimal representations use fewer digits than binary making it easier to express values

D. Hexadecimal representations use fewer digits than binary making it easier to express values

Why is A the correct answer choice?

One way to approach this problem is to take each of the three decimal numbers from the RGB value and first convert them to an 8-bit binary number (a byte). For example, the red value of 21 would be converted as follows: (0)(128)+(0)(64)+(0)(32)+(1)(16)+(0)(8)+(1)(4)+(0)(2)+(1)(1) So, the decimal number 21 is equivalent to the binary number 0001 0101. To convert a binary number to hexadecimal format, break up the number into groups of 4 bits starting from the right. The least significant digit on the right represents the 2^0 position, the digit left of that represents the 2^1 position, the digit left of that represents the 2^2 position, etc. Treat each group of 4 bits as an independent binary number and express each group as a hexadecimal number, then append them together. For example the rightmost group of 4 bits from the right is (0)(8)+ (1)(4)+ (0)(2) + (1)(1) = 4 + 1 = 5 in decimal which is 5 in hexadecimal format. Since the binary number 0001 is equivalent to the hexadecimal number 1, and the binary number 0101 is equivalent to the hexadecimal number 5, the red value has the hex value of 15. Using this same approach for the green and blue values yields a hexcode of #153c2e. RGB: (21, 60, 46)

Why did contestant D win the competition?

The vote count of Contestant D is 00111. The rightmost three bits are the judges' votes which are worth twice as much as the online or live audience votes. Each of the judges' votes can be multiplied by 2 so that they are weighted properly. In this case all three judges gave the contestant a "thumbs up" so the judges' weighted the vote is (2)(3)=6. Since the live audience and online votes were both "thumbs down", the total weighed vote for contestant D is 6, which is the highest of all four contestants.

How to you turn 1001 1111 1011 0010 into hexadecimal?

To convert a binary number into hexadecimal format, break up the number into groups of 4 bits starting from the right. The least significant digit on the right represents the 2^0 position, the digit left of that represents the 2^1 position, the digit left of that represents the 2^2 position, etc. Treat each group of 4 bits as an independent binary number and express each group as a hexadecimal number, then append them together. For example, the second group of 4 bits from the right (1011) is equivalent to (1)(2^3)+(0)(2^2)+(1)(2^1)+(1)(2^0) = 8+2+1=11 in decimal

Why can 16^6 colors can be represented in the color code scheme?

Using this color code scheme, #000000 to #FFFFFF can be represented, which means that each place/digit could take on 16 values (0-F). There are 6 placeholders for values (#RRGGBB) so the total number of colors that can be represented is the following: 16x16x16x16x16x16 = 16^6