1. the word bit is a contraction for what two words?
2. explain how the terms bit, byte, nibble, and word are related.
3. why are binary and decimal called positional numbering systems?
4. what is a radix?

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Accepted Answer

### Question 1
# Brief Explanations:
The term "bit" is a contraction of "binary" and "digit". In computer science, a bit represents the smallest unit of data, which can have a value of 0 or 1, related to binary (base - 2) numbering, and "digit" refers to a single numerical symbol.
# Answer:
"binary" and "digit"

### Question 2
# Brief Explanations:
- **Bit**: The basic unit of digital information, can be 0 or 1.
- **Nibble**: A group of 4 bits. For example, the binary number 1010 is a nibble.
- **Byte**: A group of 8 bits (or 2 nibbles). It is a common unit for measuring data size, e.g., a character in ASCII is usually stored in 1 byte.
- **Word**: The number of bits that a computer's processor can handle at once. Its size (e.g., 16 - bit, 32 - bit, 64 - bit) varies by computer architecture. A word is made up of multiple bytes, and thus multiple nibbles and bits. So, bits are the building blocks, nibbles are groups of 4 bits, bytes are groups of 8 bits, and words are groups of bytes (with the number of bytes depending on the system) used for processing.
# Answer:
- Bit: Basic 0/1 data unit.
- Nibble: 4 - bit group.
- Byte: 8 - bit group (2 nibbles).
- Word: Processor - handled bit group (multiple bytes). Bits → nibbles → bytes → words (with words being for processing, built from smaller units).

### Question 3
# Brief Explanations:
In a positional numbering system, the value of a digit depends on its position (or place) within the number.
- **Decimal (base - 10)**: For example, in the number 123, the digit '1' is in the hundreds place (representing $1\times10^{2}$), '2' is in the tens place ($2\times10^{1}$), and '3' is in the ones place ($3\times10^{0}$). The value of each digit is determined by multiplying the digit by $10$ raised to the power of its position (starting from 0 at the right - most digit).
- **Binary (base - 2)**: For example, in the binary number 101, the right - most '1' is in the $2^{0}$ place ($1\times2^{0}$), the '0' is in the $2^{1}$ place ($0\times2^{1}$), and the left - most '1' is in the $2^{2}$ place ($1\times2^{2}$). The value of each bit (digit in binary) is determined by multiplying the bit (0 or 1) by $2$ raised to the power of its position. So, both binary and decimal are positional because the value of each digit/bit is determined by its position relative to the other digits/bits in the number, with the base (10 for decimal, 2 for binary) determining the place - value multiplier.
# Answer:
In binary and decimal, a digit/bit's value depends on its position. In decimal, digits are multiplied by $10^{\text{position}}$; in binary, bits by $2^{\text{position}}$, so they are positional numbering systems.

### Question 4
# Brief Explanations:
The radix (also known as the base) of a numbering system is the number of unique digits (including zero) used in that system to represent numbers. For example:
- In the decimal (base - 10) system, the radix is 10, and the digits used are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
- In the binary (base - 2) system, the radix is 2, and the digits used are 0 and 1.
- In the hexadecimal (base - 16) system, the radix is 16, and the digits used are 0 - 9 and A - F (where A = 10, B = 11, C = 12, D = 13, E = 14, F = 15). The radix determines the place - value of digits in a positional numbering system (e.g., in base $b$, the place - value of a digit in position $n$ is $b^{n}$).
# Answer:
A radix (base) is the number of unique digits (including 0) in a numbering system, determining digit place - value (e.g., base 10 for decimal, base 2 for binary).

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