Digital Numbers and Arithmetics

Vocabulary flashcards covering number systems, binary arithmetic, bitwise shifts, 1's complement representation, and character encoding standards from Lecture 3 of Computer Skills & Applications.

Analog System

A system in which physical quantities or signals may vary continuously over a specified range.

Digital System

A system in which physical quantities or signals can assume only discrete values.

Analog Signal vs. Digital Signal

An analog signal represents a continuously varying physical quantity over time, whereas a digital signal consists of discrete values sampled at distinct time intervals.

Base (Radix)

The number of unique digits available in a number system (e.g., Base $2$ for binary, Base $8$ for octal, Base $10$ for decimal, and Base $16$ for hexadecimal).

Bit

A single binary digit, taking a value of either $0$ or $1$.

Byte

A unit of digital data consisting of a sequence of $8$ bits.

Word

A unit of computer memory consisting of $2$ bytes ($16$ bits).

Most Significant Bit (MSB)

The first bit from the left in a byte, located at Position number $7$.

Least Significant Bit (LSB)

The last bit from the left in a byte, located at Position number $0$.

Octal System

A Base-$8$ number system that uses the set of digits $\{0, 1, 2, 3, 4, 5, 6, 7\}$.

Hexadecimal System

A Base-$16$ number system that uses digits $\{0, 1, 2, 3, 4, 5, 6, 7, 8, 9\}$ and letters $\{A, B, C, D, E, F\}$, where the letters represent decimal values $10$ through $15$ to avoid confusion.

1's Complement (Bitwise NOT)

An operation where each bit in a binary number is subtracted from $1$ (inverting each $0$ to a $1$ and each $1$ to a $0$), denoted as $\text{NOT}(A) = \overline{A}$.

End-Around Carry

A carry arising from the most significant bit during binary subtraction using 1's complement; when it equals $1$, the result is positive and the carry must be added to the sum to obtain the final answer.

Bitwise Left Shift ($<<$)

An operation that pushes bits to the left and fills the vacated positions on the right with $0$, effectively multiplying the binary value by $2$ ($\text{mod } 2^4$) for each shift.

Bitwise Right Shift ($>>$)

An operation that pushes bits to the right and fills each vacated position on the left with $0$, effectively performing integer division by $2$ ($\text{mod } 2^4$) for each shift.

Binary-Coded Decimal (BCD)

An encoding system where each individual decimal digit is represented by its own separate $4$-bit binary code, commonly used in digital displays and data conversion.

Reflected Binary (Gray) Code

A binary code in which only a single bit changes between consecutive decimal numbers, utilizing a symmetric construction and commonly applied in rotary encoding.

Standard ASCII

The American Standard Code for Information Interchange using $7$ bits per character, capable of representing $2^7 = 128$ characters.

Extended ASCII

An extension of the ASCII character encoding standard using $8$ bits per character, capable of representing $2^8 = 256$ characters.

Unicode

A character encoding standard using $16$ bits per character capable of representing $2^{16} = 65{,}536$ characters (approximately $65{,}000$), incorporating standard ASCII alongside characters and symbols from international alphabets like Greek, Chinese, and Arabic.