Glossary

AI-1

Appendix I

GLOSSARY ADDEND ¾ A number to be added to an augend. ADDITION ¾ A form of counting where on quantity is added to another. AND GATE ¾ A logic circuit in which all inputs must be HIGH to produce a HIGH output. ASSOCIATIVE LAW ¾ A simple equality statement A(BC) = ABC or A+(B+C) = A+B+C. AUGEND ¾ A number to which another number is to be added. BASE ¾ The number of symbols used in the particular number system. BCD (BINARY CODED DECIMAL) ¾ A method of using binary digits to represent the decimal digits 0 through 9. BINARY SYSTEM ¾ The base 2 number system using 0 and 1 as the symbols.

BOOLEAN ALGEBRA ¾ A mathematical concept based on the assumption that most quantities have two possible conditions ¾ TRUE and FALSE. BOOLEAN EXPRESSION ¾ A description of the input or output conditions of a logic gate. BORROW ¾ To transfer a digit (equal to the base of the number system) from the next higher order column for the purpose of subtraction. CARRY ¾ A carry is produced when the sum of two or more numbers in a vertical column equals or exceeds the base of the number system in use. CLOCK ¾ A circuit that generates timing control signals in a computer or other type of digital equipment.

COMMUTATIVE LAW ¾ The order in which terms are written does not affect their value; AB = BA, A+B = B+A. COMPATIBILITY ¾ The feature of logic families that allows interconnection of circuits without the need for additional circuitry. COMPLEMENT ¾ Something used to complete something else. COMPLEMENTARY LAW ¾ A term ANDed with its complement is 0, and a term ORed with its complement is 1; A A = 0, A + A = 1. CONVERSION ¾ To change a number in one base to its equivalent in another base. COUNTER ¾ A device that counts.

D FLIP-FLOP ¾ Stores the data bit (D) in conjunction with the clock input. DECADE COUNTER ¾ Counter from 0 to 1010 in base 2, then resets. DECIMAL POINT ¾ The radix point for the decimal system. AI-2 DECIMAL SYSTEM ¾ A number system with a base or radix of 10. DEMORGAN’S THEOREM ¾ This theorem has two parts: the first states that AB = A + B ; the second states that BA + = A B . DIFFERENCE ¾ That which is left after subtraction. DISTRIBUTIVE LAW ¾ (1) a term (A) ANDed with a parenthetical expression (B+C) equals that term ANDed with each term within the parenthesis: A(B+C) = AB+AC; (2) a term (A) ORed with a parenthetical expression (BC) equals that term ORed with each term within the parenthesis: A+(BC) = (A+B)(A+C).

DIVIDEND ¾ A number to be divided. DIVISOR ¾ A number by which a dividend is divided. DOUBLE NEGATIVE LAW ¾ A term that is inverted twice is equal to the term; A = A. DOWN COUNTER¾ A circuit that counts from a predetermined number down to 0. EXCLUSIVE-NOR (X-NOR) ¾ A logic circuit that produces a HIGH output when all inputs are LOW or all inputs are HIGH. EXCLUSIVE-OR (X-OR) GATE ¾ A logic circuit that produces a HIGH output when one and only one input is HIGH. EXPONENT ¾ A number above and to the right of a base indicating the number of time the base is multiplied by itself; 24 = 2 · 2 · 2 · 2.

FLIP-FLOP ¾ A bistable multivibrator. FRACTIONAL NUMBER ¾ A symbol to the right of the radix point that represents a portion of a complete object. HEXADECIMAL (HEX) SYSTEM ¾ The base 16 number system using 0 through 9 and A, B, C, D, E, and F as symbols. IDEMPOTENT LAW ¾ States that a term ANDed with itself or ORed with itself is equal to the term; AA = A, A+A = A. INVERTER ¾ A logic gate that outputs the complement of its input. J-K FLIP-FLOP ¾ Can perform the functions of the RS, T, and D flip-flops. LAW OF ABSORPTION ¾ This law is the result of the application of several other laws. It states that A(A+B) = A or A+(AB) = A.

LAW OF COMMON IDENTITIES ¾ The two statements A( A +B) = AB and A+ A B = A+B are based on the complementary law. LAW OF IDENTITY ¾ States that a term TRUE in one part of an expression will be TRUE in all parts of the expression; A = A, A = A . LAW OF INTERSECTION ¾ A term ANDed with 1 equals that term, and a term ANDed with 0 equals 0; A·1 = A, A· 0 = 0. AI-3 LAW OF UNION ¾ A term ORed with 1 equals 1; a term ORed with 0 equals that term; A+1 = 1, A + 0 = 0. LEAST SIGNIFICANT (LSD) ¾ The digit which has the least effect on the value of a number.

LOGIC ¾ The science of reasoning; the development of a reasonable or logical conclusion based on known information. LOGIC FAMILY ¾ A group of logic circuits based on specific types of circuit elements (DTL, TTL, CMOS, and so forth). LOGIC GATES ¾ Decision-making circuits in computers and other types of equipment. LOGIC POLARITY ¾ The polarity of a voltage used to represent the logic 1 state. LOGIC SYMBOL ¾ Standard symbol used to indicate a particular logic function. MINUEND ¾ The number from which another number is subtracted.

MIXED NUMBER ¾ Represents one or more complete units and a portion of a single unit. MODULUS ¾ The number of different values that a counter can contain or display. MOST SIGNIFICANT DIGIT (MSD) ¾ The digit which if changed will have the greatest effect on the value of a number. NAND GATE ¾ An AND gate with an inverted output. The output is LOW when all inputs are HIGH, and HIGH when any or all inputs are LOW. NEGATIVE LOGIC ¾ The voltage representing logic state 1 is more negative that the voltage representing a logic state 0.

NEGATOR ¾ See inverter. NOR GATE ¾ An OR gate with an inverted output. The output is LOW when any or all inputs are HIGH, and HIGH when all inputs are LOW. NOT CIRCUIT ¾ See inverter. NUMBER ¾ A symbol used to represent a unit or a quantity. OCTAL SYSTEM ¾ The base 8 number system using 0 through 7 as the symbols. OR GATE ¾ A logic circuit which produces a HIGH output when one or more inputs is/are HIGH. PARALLEL DATA ¾ Each bit of data has a separate line and all bits are moved simultaneously. PARALLEL REGISTER ¾ A register that receives, stores, and transfers data in a parallel mode.

POSITIONAL NOTATION ¾ A method where the value of the number is defined by the symbol and the symbol’ s position. POSITIVE LOGIC ¾ The voltage representing logic state 1 is more positive than the voltage representing a logic state 0. POWER OF A NUMBER ¾ The number of times a base is multiplied by itself. The power of a base is indicated by the exponent; that is, 103 = 10 ·10 ·10. AI-4 QUOTIENT ¾ The result in division. RADIX POINT ¾ The symbol that separates whole numbers and fractional numbers. RADIX ¾ The total number of symbols used in a particular number system.

REGISTER ¾ A circuit of flip-flops designed to receive, store, and transfer data. REMAINDER ¾ The final undivided part that is less than the divisor. RING COUNTER ¾ A loop in which only one flip-flop will be set at any given time; used in timing. RIPPLE (ASYNCHRONOUS) COUNTER ¾ A circuit that counts from 0 to a specified value. Subject to error at high frequency. R’s (RADIX) COMPLEMENT ¾ The difference between a given number and the next higher power of the number system (10008 minus 2548 equals 5248). R’s-1 (RADIX-1) COMPLEMENT ¾ The difference between a given number and the highest value symbol in the number system (7778 minus 2548 equals 5248).

R-S FLIP-FLOP ¾ A flip-flop with two inputs ¾ S (set) and R (reset). The Q output is HIGH in the set mode and LOW in the reset mode. SERIAL DATA ¾ All data bits are transferred one bit at a time along a single conductor. SHIFT REGISTER ¾ A register capable of serial-to-parallel and parallel-to-serial conversion and scaling. SHIFTING ¾ Moving the contents of a register right or left to scale the number or to input or output serial data. SUBSCRIPT ¾ A number written below and to the right of a value indicating the base or radix of the number system in use (358).

SUBTRACTION ¾ Taking away one number from another. SUBTRAHEND ¾ The quantity to be subtracted from the minuend. SUM ¾ The result in addition. SYNCHRONOUS COUNTER ¾ Performs the same function as a ripple counter but error free at high frequency. T FLIP-FLOP ¾ A single input flip-flop that changes state with each positive pulse or each negative pulse. Divides input frequency by two. TRUTH TABLE ¾ A chart showing all possible input combinations and the resultant outputs. UNIT ¾ A single object. UP/DOWN COUNTER ¾ A counter circuit that can count up or down on command.

VINCULUM ¾ A bar over a logic statement indicating the FALSE condition of the statement. WHOLE NUMBER ¾ A symbol that represents one or more complete objects. ZERO ¾ A symbol that indicates no numerical value for a position in positional notation.