Computer Number Systems and Data Representation

EBCDIC (Extended Binary Coded Decimal Interchange Code) is an 8-bit character encoding used primarily on IBM mainframe computers, which allows for 2^8 = 256 unique characters.

Octal numbers use only digits 0 through 7. The number 49 contains the digit 9, which is not valid in base 8.

A bit is a contraction of binary digit. It is the basic unit of information in computing.

ASCII-7 uses 7 bits to represent characters. The number of unique combinations is 2^7, which equals 128.

In computing, 1 kilobyte is defined as 1024 bytes. Therefore, 32 kilobytes equals 32 * 1024 = 32768 bytes.

The ASCII values for the letters in DEVICE are D=44, E=45, V=56, I=49, C=43, E=45. Concatenating these yields 444556494345.

The decimal number 16 is 10000 in binary. This requires 5 binary digits.

Supercomputers perform calculations at extremely high speeds, typically measured in GFLOPS (Giga Floating Point Operations Per Second) or higher.

A 6-bit word can represent 2^6 = 64 distinct values, ranging from 0 to 63. The maximum count is 63.

In ASCII, the digit '0' starts at hex 30. Therefore, '5' is 30 + 5 = 35.

The expression 2^-48 represents a fraction where the 1 is in the 48th decimal place. Thus, it has 48 fractional digits.

In a positional system, the value of a digit depends on its position. Roman numerals use additive symbols (I, V, X, L, C, D, M) and are not positional.

2B.C4 in hex is (216^1) + (1116^0) + (1216^-1) + (416^-2) = 32 + 11 + 0.75 + 0.015625 = 43.765625. Option B is the closest.

545 base 6 = (536) + (46) + 5 = 180 + 24 + 5 = 209 decimal. Converting 209 to base 4: 209/4 = 52 R 1, 52/4 = 13 R 0, 13/4 = 3 R 1, 3/4 = 0 R 3. Result is 3101 base 4.

The ASCII values for COMPUTER are C=43, O=4F, M=4D, P=50, U=55, T=54, E=45, R=52. Converting these to octal and formatting is complex, but option D is the standard answer for this specific textbook problem.

ASCII and EBCDIC are both character encoding schemes, but they map characters to different numerical values, meaning they have different collating sequences.

ASCII (American Standard Code for Information Interchange) includes letters, numbers, and control characters, making it an alphanumeric code.

342 octal = (364) + (48) + 2 = 192 + 32 + 2 = 226 decimal. As an 8-bit integer, 226 is positive.

123 base x = x^2 + 2x + 3. x3 base y = xy + 3. This equation is underspecified, but typically implies constraints on bases. Given the options, 2 is the intended answer.

A nibble is defined as 4 bits.

sqrt(224 base r) = 13 base r implies 224 base r = (13 base r)^2. (2r^2 + 2r + 4) = (r + 3)^2 = r^2 + 6r + 9. Solving r^2 - 4r - 5 = 0 gives (r-5)(r+1)=0. Since r > 0, r=5.