1. HCL and ALU תרגול 10

2. Overview of Logic Design Fundamental Hardware Requirements – Communication: How to get values from one place to another – Computation – Storage Bits are Our Friends – Everything expressed in terms of values 0 and 1 – Communication Low or high voltage on wire – Computation Compute Boolean functions – Storage Store bits of information

3. Digital Signals – Use voltage thresholds to extract discrete values from continuous signal – Simplest version: 1-bit signal Either high range (1) or low range (0) With guard range between them – Not strongly affected by noise or low quality circuit elements Can make circuits simple, small, and fast Voltage Time 0 1 0

4. HCL (hardware control language) HCL HCL - - A programming language used to develop and understand the control logic of processor architecture. - - Describes the control logic of different processor design. Logic Gate Types Logic Gate Types - - Logic gates are always active - Input →... time → output Voltage Time a b a && b Rising Delay Falling Delay

5. Combinational Circuits and HCL Combinational circuit Combinational circuit - - Combination of logic gates - Output cannot be connected together - Acyclic Combinational circuit to test for bit equality Combinational circuit to test for bit equality - The output will equal 1 when both inputs are 0, or both are 1. HCL code : Bool eq = (a && b) || (!a && !b)

6. Combinational Circuits and HCL Multiplexor - Sets a value depending on a control input signal - The output will equal a when s is 1, and b when s is 0. HCL code : Bool out = (s && a) || (!s && b)

7. Combinational Circuits and HCL HCL versus C - Change occurs over time - There is no real assignment, just assignment to expressions - Expressions cannot be partially evaluated Example: (a && !a) && func(b,c)

8. Combinational Circuits and HCL Word-level equality test circuit HCL code : Bool EQ = ( A == B)

9. Combinational Circuits and HCL Word-level multiplexor HCL (case expression) - 1 stands for default

10. Combinational Circuits and HCL Mux 4 int Out4 = [ !s1 && !s0 : A; !s1 : B; s1 && !s0 : C; 1 : D; ]; Min 3 int Min3 = [ A <= B && A <= C : A; B <= A && B <= C : B; 1 : C; ];

11. Arithmetic Logic Unit An arithmetic and logic unit (ALU) is a digital circuit that performs arithmetic and logical operations. The ALU is a fundamental building block of the Central Processing Unit of a computer, and even the simplest microprocessors contain one for purposes such as maintaining timers. The processors found inside modern CPUs and graphics processing units (GPUs) accommodate very powerful and very complex ALUs; a single component may contain a number of ALUs. 11

12. OF ZF CF OF ZF CF OF ZF CF OF ZF CF Arithmetic Logic Unit Combinational logic Continuously responding to inputs Control signal selects function computed Corresponding to 4 arithmetic/logical operations in Y86 Addition, Subtraction, AND, OR Also computes values for condition codes ALUALU Y X X + Y 0 ALUALU Y X X - Y 1 ALUALU Y X X & Y 2 ALUALU Y X X ^ Y 3 A B A B A B A B

13. The basic ALU provides the basic logical and arithmetic functions: AND, OR plus addition. Shift, multiplication and division are usually outside the basic ALU. Logical operations 1 bit logical unit for AND/OR operations select (AND or OR) result 0101 MUX abab Basic ALU (Combinational Circuit)

14. The ALU ALU includes combinational logic. – Combinational logic  a change in inputs directly causes a change in output, after a characteristic delay. – Different from sequential logic which only changes on the clock. Two major components of combinational logic are – multiplexors & decoders which we previously talked about. 0123456701234567 c 3 X 8 multiplexor s1 s2 0123456701234567 DECODER 012012 3 X 8 Decoder s0

15. abC in sumC out 00000 00110 01010 01101 10010 10101 11001 11111 inputs outputs sum = (a  b  C in ) + (a  b  C in ) + (a  b  C in ) + (a  b  C in ) = a + b + C in C out =(b  C in ) + (a  C in ) + (a  b) = ((a + b)  C in ) + (a  b) abab C out C in Adder hardware for C out in 2 layers 1 bit FULL adder (3,2) ab C in C out sum Carry in Carry out

16. Full Adder from Half Adders Half adder Full adder from 2 half adders + or gate abab Cout sum Cin abab Cout sum

17. 1 bit simple ALU for logical / arithmetic operations - does not yet include subtraction. abab select result 012012 + 2 Cin Cout 1 Bit Simple ALU

18. Enhanced for subtraction abab select result 012012 + 2 Cin Cout invert 1's complement For subtraction use Cin = 1 and inverse b subtraction: a + b + 1 = a + (b + 1) = a + (-b) = a - b 0101 1 Bit Enhanced ALU

19. Ripple Carry Type Adder To produce a 32 bit result, we connect 32 single bit units together. This type of ALU adder is called a ripple adder – Carry bits are generated in sequence. – Bit 31 result and Cout is not correct until it receives Cin from previous unit, which is not correct until it receives Cin from its previous unit, etc. – Total operation time is proportional to word size (here 32). a0 b0 result 0 Cin Cout Cin ALU0 Cout Cin ALU1 Cout Cin ALU2 Cout Cin ALU31 Cout...... a1 b1 a2 b2 a31 b31 result 1 result 2 result 31...... operation = invert + select 32 bit ADDER with ripple carry: 3