Binary System — Set 5

Correct Answer: B. Binary Digit

• **Binary Digit** = the full form of 'bit,' coined by John Tukey in 1947 and popularized by Claude Shannon. A bit is the most elementary unit of information in computing, representing a single binary value of 0 or 1. • **Shannon's role** — in his landmark 1948 paper 'A Mathematical Theory of Communication,' Shannon used 'bit' to quantify information, defining it as the amount of information in a fair coin flip (yes/no, 0/1). • Everything a computer stores — documents, photos, programs — is ultimately a long sequence of individual binary digits (bits). • Option A (Binary Integer) is wrong because a binary integer is a multi-bit number, not a single digit; Option C (Bipolar Technology) is wrong because bipolar refers to a transistor manufacturing process, unrelated to the word 'bit'; Option D (Binary Interval) is wrong because this term does not exist in computing.

Correct Answer: A. 8

• **8** = the number of bits in a single byte. This 8-bit grouping became the universal standard in the 1970s because it is large enough to encode all ASCII characters and aligns with powers of 2 in memory addressing. • **Historical note** — early computers used 6-bit or 7-bit 'bytes,' but the IBM System/360 (1964) standardized the 8-bit byte, and it has remained universal ever since. • A byte holds 2⁸ = 256 unique values, enough for a single character in ASCII (128 codes) or extended ASCII (256 codes). • Option B (4) is wrong because 4 bits form a nibble, half a byte; Option C (16) is wrong because 16 bits form a word (2 bytes); Option D (32) is wrong because 32 bits form a double-word (4 bytes).

Correct Answer: C. Binary

• **Binary** = the name of the base-2 number system, derived from the Latin word 'binarius' meaning 'consisting of two.' It is the foundational number system of all digital computers because electronic circuits naturally operate in two states: on (1) and off (0). • **Why base 2?** — transistors, the building blocks of CPUs, act as switches with two stable states (conducting vs. non-conducting), making binary the most reliable and noise-resistant encoding for digital hardware. • Every higher-level number system used in computing (octal, hex) is simply a shorthand for grouping binary digits into more human-readable chunks. • Option A (Decimal) is wrong because decimal is base 10, the number system humans use naturally; Option B (Hexadecimal) is wrong because hexadecimal is base 16; Option D (Octal) is wrong because octal is base 8.

Correct Answer: B. 0 and 1

• **0 and 1** = the only two digits used in the binary number system. These two symbols correspond to the two stable voltage states in electronic circuits — low voltage (0) and high voltage (1) — making binary the natural language of digital hardware. • **No other digits** — binary's base is 2, so valid digits are 0 through (base-1) = 0 through 1. Any attempt to write '2' or higher in binary is a notation error. • All letters, numbers, images, and sounds in a computer are encoded as sequences of these two digits — billions of 0s and 1s processed every second. • Option A (1 and 2) is wrong because '2' is not a binary digit; the binary base is 2, so digits only go up to 1; Option C (0 to 9) is wrong because 0–9 are the ten digits of the decimal system, not binary; Option D (A and B) is wrong because A and B are hexadecimal digits (values 10 and 11), not binary.

Correct Answer: B. 4

• **4** = the decimal equivalent of binary 100. Calculation: 100 → (1×2²) + (0×2¹) + (0×2⁰) = (1×4) + 0 + 0 = 4. • **Pattern recognition** — binary 100 has a 1 only in the third position (weight 4), so its decimal value equals exactly 4, the second power of 2 (2²). • Any binary number of the form 1 followed by n zeros equals 2ⁿ in decimal: 10=2, 100=4, 1000=8, 10000=16, and so on. • Option A (2) is wrong because binary 10 = 2, not 100; Option C (8) is wrong because binary 1000 = 8, which has four digits; Option D (10) is wrong because decimal 10 = binary 1010, a four-bit number.

Correct Answer: B. 7

• **7** = the decimal equivalent of binary 111. Calculation: 111 → (1×2²) + (1×2¹) + (1×2⁰) = 4+2+1 = 7. • **All-ones pattern** — when all bits in a group are 1, the decimal value equals 2ⁿ-1 where n is the number of bits: 1-bit 1=1, 2-bit 11=3, 3-bit 111=7, 4-bit 1111=15. • 7 is the maximum value of a 3-bit unsigned integer and corresponds to the hexadecimal digit 7 and the octal digit 7. • Option A (3) is wrong because binary 11 = 3 (only 2 digits, not 3); Option C (8) is wrong because binary 1000 = 8, which requires 4 bits; Option D (15) is wrong because binary 1111 = 15, which has 4 bits.

Correct Answer: C. NOT Gate

• **NOT Gate** = the logic gate used to invert a binary digit, turning 0 into 1 and 1 into 0. It is a single-input, single-output gate — the simplest logic element — and is called an 'inverter' in circuit design. • **Circuit symbol** — the NOT gate is drawn as a triangle pointing right with a small circle (bubble) at its output tip, where the bubble universally indicates inversion. • Inverters are essential for generating complementary signals, enabling flip-flop memory cells, and forming the basis of all other gates when combined (NOT+AND=NAND, NOT+OR=NOR). • Option A (AND Gate) is wrong because AND takes two inputs and produces a conjunction, not an inversion; Option B (OR Gate) is wrong because OR outputs 1 if any input is 1, not a single-bit flip; Option D (XOR Gate) is wrong because XOR compares two inputs for difference, not a single-input inversion.

Correct Answer: B. Nibble

• **Nibble** = the standard name for a group of exactly 4 bits, half of a byte. The term is a playful diminutive of 'byte' — just as a nibble is a small bite, a nibble is half a byte. • **Hex connection** — one nibble maps to exactly one hexadecimal digit (0–F) because 2⁴ = 16, the same as hex's base, making nibbles the natural unit for hex-to-binary conversion. • In BCD (Binary-Coded Decimal) encoding, each decimal digit (0–9) is stored in its own nibble, using 4 bits per digit in financial and measurement applications. • Option A (Byte) is wrong because a byte is 8 bits (two nibbles); Option C (Word) is wrong because a word is 16 or 32 bits depending on the CPU architecture; Option D (Kilobit) is wrong because a kilobit is 1000 or 1024 bits, a storage size unit, not a 4-bit grouping name.

Correct Answer: A. AND Gate

• **AND Gate** = a logic gate that outputs 1 only when ALL of its inputs are 1. For two inputs, this means only the combination (1,1) produces a 1 output; all other pairs — (0,0), (0,1), (1,0) — produce 0. • **Hardware** — an AND gate is physically built with two transistors connected in series; current flows to the output only when both transistors conduct simultaneously, directly modeling the AND truth table. • AND gates are the foundation of binary multiplication and bit-masking operations in CPUs, used to selectively read individual bits from a register. • Option B (OR Gate) is wrong because OR outputs 1 whenever at least one input is 1, not only when both are 1; Option C (XOR Gate) is wrong because XOR outputs 1 only when inputs are different, not when both are 1; Option D (NAND Gate) is wrong because NAND outputs 0 only when both inputs are 1 — the opposite of AND.

Correct Answer: C. 10

• **10** = the decimal value of binary 1010. Calculation: 1010 → (1×2³)+(0×2²)+(1×2¹)+(0×2⁰) = 8+0+2+0 = 10. • **Positional breakdown** — the '1' in position 4 (weight 8) and the '1' in position 2 (weight 2) are the active bits; the zeros in positions 3 and 1 contribute nothing. • Verification: 8+2 = 10. This is also the same as decimal 10, which is why 1010 is one of the most tested binary-to-decimal conversions. • Option A (5) is wrong because binary 0101 = 5, not 1010; Option B (8) is wrong because binary 1000 = 8, which has only the 8-position bit set; Option D (12) is wrong because binary 1100 = 8+4 = 12.