# ECEN 468 Advanced Logic Design

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1 ECEN 468 Advanced Logic Design Lecture 26: Verilog Operators ECEN 468 Lecture 26

2 Operators Operator Number of Operands Result Arithmetic 2 Binary word Bitwise 2 Binary word Reduction 1 Bit Logical 2 Boolean value Relational 2 Boolean value Shift 1 Binary word Conditional 3 Expression ECEN 468 Lecture 26 2

3 Arithmetic Operators v 2 s complement representation v MSB is sign bit v For scalar and vector v For nets and registers Symbol Operator + Addition - Subtraction * Multiplication / Division % Modulus ECEN 468 Lecture 26 3

4 Bitwise Operators ~(101011) = (010101) & (001100) = (010101) ^ (001100) = Shorter word will extend to the size of longer word by padding bits with 0 Symbol Operator ~ Bitwise negation & Bitwise and Bitwise inclusive or ^ Bitwise exclusive or ~^, ^~ Bitwise exclusive nor ECEN 468 Lecture 26 4

5 Reduction Operators &(101011) = 0 (001100) = 1 Symbol & ~& Operator Reduction and Reduction nand v Unary operators v Return single-bit value Reduction or ~ Reduction nor ^ ~^, ^~ Reduction xor Reduction xnor ECEN 468 Lecture 26 5

6 Logical Operators v Case equality operators detect exact bit-by-bit match, including x or z v The logical equality operator is less restrictive, x is returned for any ambiguity v Verilog is loosely typed - OK to use A&&B when A and B are vectors o A&&B returns true if both words are non-zero integers v === can recognize x and z while == would return x for ambiguity Symbol Operator! Logical negation && Logical and Logical or == Logical equality!= Logical inequality === Case equality!== Case inequality ECEN 468 Lecture 26 6

7 Relational and Shift Operators Relational operators Shift operators < << <= >> > >= v Relational operators return x for ambiguity v 0xxx > 1xxx returns 1 if ( ( a < b ) && ( a >= c ) ) result = a << 3; ECEN 468 Lecture 26 7

8 Conditional Operator Y = ( A == B )? C : D; wire [1:0] select; wire [15:0] D1, D2, D3, D4; wire [15:0] bus = (select == 2 b00)? D1 : (select == 2 b01)? D2 : (select == 2 b10)? D3 : (select == 2 b11)? D4 : 16 bx? : 0 1 X 0 0 X X 1 X 1 X X X X X v z is not allowed in conditional_expression v If conditional_expression is ambiguous, both true_expression and false_expression are evaluated bitwisely according to the truth table to get the result ECEN 468 Lecture 26 8

9 Operands v A Verilog operand may be compose of o Nets o Registers o Constants o Numbers o Bit-select of a net or a register o Part-select of a net or a register o A function call o Concatenation of any of above ECEN 468 Lecture 26 9

10 Operator Precedence Operator precedence Highest Operator symbol -! ~ (unary) * / % + - (binary) << >> < <= > >= ==!= ===!== & ~& ^ ^~ ~^ ~ && Lowest? : Parentheses for precaution! ECEN 468 Lecture 26 10

11 Synthesis of Arithmetic Operators v If corresponding library cell exists, an operator will be directly mapped to it v Synthesis tool may select among different options in library cell, for example, when synthesize an adder o Small wordlength -> ripple-carry adder o Long wordlength -> carry-look-ahead adder o Need small area -> bit-serial adder v Implementation of * and / o May be inefficient when both operands are variables o If a multiplier or the divisor is a power of two, can be implemented through shift register ECEN 468 Lecture 26 11

12 Synthesis of Shift Operators v Synthesis tools normally support shifting by a constant number of bits v Cannot support a variable shift ECEN 468 Lecture 26 12

13 Relational Operators Relational operators ( <, >, >=, <= ) can be implemented through o Combinational logic o Adder/subtractor In bit-extended format Calculate A B, check extended bit of result 0 -> A >= B 1 -> A < B module compare ( lt, gt, eq, A, B ); input A, B; output lt, gt, eq; assign lt = ( A < B ); assign gt = ( A > B ); assign eq = ( A == B ); endmodule ECEN 468 Lecture 26 13

14 Synthesis of Identity Operators v The logical identity operators ( ==,!= ) and the case identity operators ( ===,!== ) are normally synthesized to combinational logic ECEN 468 Lecture 26 14

15 Reduction, Bitwise and Logical Operators v They are translated into a set of equivalent Boolean equations and synthesized into combinational logic ECEN 468 Lecture 26 15

16 Conditional Operator v The conditional operator (? : ) synthesizes into library muxes or gates that implement the functionality of a mux v The expression to the left of? is formed as control logic for the mux ECEN 468 Lecture 26 16

17 Concatenation Operator v Equivalent to a logical bus v No functionality of its own v Generally supported by synthesis tool ECEN 468 Lecture 26 17

18 Grouping of Operators module operator_group ( sum1, sum2, a, b, c, d ); input a, b, c, d; output sum1, sum2; assign sum1 = a + b + c + d; assign sum2 = ( a + b ) + ( c + d ); endmodule b a c adder adder adder d adder adder sum2 adder sum1 ECEN 468 Lecture 26 18

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