Discreet Math - Chapter 2.5 - " Application: Number Systems and Circuits for Addition" FLASHCARDS

Vocabulary practice flashcards covering base number systems, binary arithmetic circuits, two's complements, and hexadecimal representations.

Decimal Notation

A base-$10$ number system that expresses a number as a string of digits in which each digit's position indicates the power of $10$ by which it is multiplied.

Binary Notation

A base-$2$ number system in which any positive integer is represented uniquely as a sum of products of the form $d \frac{}{}$ where each binary digit $d$ is either $0$ or $1$.

Bit

A single binary digit, which can hold a value of either $0$ or $1$.

Half-Adder

A circuit designed to compute the sum of two binary digits $P$ and $Q$, outputting a carry bit defined by $P \wedge Q$ and a sum bit defined by $(P \lor Q) \wedge \sim(P \wedge Q)$.

Full-Adder

A circuit designed to compute the sum of three binary digits ($P$, $Q$, and $R$) to produce a carry output $C$ and a sum output $S$.

Parallel Adder

A circuit constructed using full-adders and/or half-adders capable of adding multi-digit binary numbers of any finite length.

8-Bit Two's Complement (for a Nonnegative Integer)

The $8$-bit binary representation for an integer $a$ where $0 \le a \le 127$.

8-Bit Two's Complement (for a Negative Integer)

The $8$-bit binary representation for $2^8 - |a|$ where $-128 \le a < 0$, obtained by writing the $8$-bit binary form of $|a|$, flipping all bits, and adding $1$ in binary.

Overflow Error

An error occurring when an arithmetic calculation yields a result outside the fixed bit-length system capacity of the computer.

Hexadecimal Notation

A base-$16$ number system expressing integers as sums of products of powers of $16$, using digits $0$-$9$ and letters $A$-$F$ to represent numbers $10$ through $15$.

Byte

The smallest addressable memory unit on most computers, consisting of $8$ bits.

Memory Dump

A display or printout of the contents of memory locations in order, typically presented in hexadecimal format to save space.