Number Representation — Practice MCQs for CCAT

Correct Answer: B — 1101

Sign-magnitude: MSB=1 (negative), remaining=5(101). -5 = 1101.

Correct Answer: A — 1001

1's complement: invert all bits. 0110 → 1001.

Correct Answer: B — 1010

2's complement = 1's complement + 1 = 1001 + 1 = 1010.

Correct Answer: A — 1001

BCD: each decimal digit in 4 bits. 9 = 1001.

Correct Answer: B — Only one bit changes between adjacent values

Gray code: adjacent values differ by only 1 bit.

Correct Answer: C — 7 or 8

ASCII uses 7 bits (standard) or 8 bits (extended).

Correct Answer: B — 1000

Excess-3: add 3 to digit then convert. 5+3=8=1000.

Correct Answer: B — Sign, exponent, mantissa

Floating point: sign bit + exponent + mantissa.

Correct Answer: B — 32 bits

IEEE 754 single precision = 32 bits.

Correct Answer: B — Error detection

Parity bit detects single-bit errors in data.

Correct Answer: B — 10

1010 = 1×8 + 0×4 + 1×2 + 0×1 = 8 + 0 + 2 + 0 = 10

Correct Answer: B — 11111011

5 = 00000101. 1's complement = 11111010. Add 1 for 2's complement = 11111011.

Correct Answer: B — -128 to +127

For n bits, 2's complement range is -2^(n-1) to +2^(n-1)-1. For 8 bits: -128 to +127.

Correct Answer: B — The sign of the number

In sign-magnitude, the Most Significant Bit (MSB) represents sign: 0 for positive, 1 for negative.

Correct Answer: B — Only one representation of zero

2's complement has only one representation of zero, while 1's complement has +0 and -0.

Correct Answer: A — F0

11110000: 1111 = F, 0000 = 0. So 11110000 = F0 in hexadecimal.

Correct Answer: A — 10100101

A = 1010, 5 = 0101. So A5 = 10100101 in binary.

Correct Answer: A — When result needs more bits than available

Overflow occurs when the result of an arithmetic operation exceeds the range that can be represented with the available bits.

Correct Answer: A — Binary Coded Decimal - 4 bits per decimal digit

BCD uses 4 binary bits to represent each decimal digit (0-9), making decimal calculations easier.

Correct Answer: B — 01000111

In BCD: 4 = 0100, 7 = 0111. So 47 = 01000111.

Correct Answer: A — 72

Group binary digits in 3s from right: 111 010 = 7 2 = 72 in octal.

Correct Answer: B — Very large or very small real numbers

Floating point allows representation of very large or very small real numbers using sign, exponent, and mantissa.

Correct Answer: B — 8

IEEE 754 single precision (32-bit): 1 sign bit, 8 exponent bits, 23 mantissa bits.

Correct Answer: A — 0101

1's complement is obtained by inverting all bits. 1010 becomes 0101.

Correct Answer: B — Universal character encoding supporting many languages

Unicode is a universal character encoding standard that supports characters from virtually all writing systems.