IKI 10201 05 bArithmetic Logic Unit ALU Bobby

IKI 10201 05 b-Arithmetic Logic Unit (ALU) Bobby Nazief Semester-I 2005 - 2006 The materials on these slides are adopted from: • CS 231’s Lecture Notes at UIUC, which is derived from Howard Huang’s work and developed by Jeff Carlyle; • Prof. Daniel Gajski’s transparency for Principles of Digital Design.

Adders/Subractors: Arithmetic Unit • • • When Sub = 0, the XOR gates output B 3 B 2 B 1 B 0 and the carry in is 0. The adder output will be A + B + 0, or just A + B. When Sub = 1, the XOR gates output B 3’ B 2’ B 1’ B 0’ and the carry in is 1. Thus, the adder output will be a two’s complement subtraction, A - B. Arithmetic Unit that is capable to do addition & subtraction can be constructed using Full Adders.

Logical Unit • • In addtion to arithmetic operations, most computers also support logical operations like AND, OR and NOT, but extended to multi-bit words instead of just single bits. To apply a logical operation to two words X and Y, apply the operation on each pair of bits Xi and Yi: 1 0 1 1 AND 1 1 1 0 1 0 OR 1 0 1 1 1 1 1 0 1 1 XOR 1 1 1 0 01 01

Defining a logic unit • • Boolean functions of 2 variables have 2 inputs, 1 output, and 4 minterms We can generate 16 Boolean functions using 4 (select) variables: the Truth Table: • Boolean Functions: – AND f 8 values of select variables S 3 S 2 S 1 S 0 = 1000 – OR f 14 values of select variables S 3 S 2 S 1 S 0 = 1110 –. . .

Logic unit implementation

Arithmetic-Logic Units (ALUs) • An arithmetic-logic unit, or ALU, performs many different arithmetic and logic operations. The ALU is the “heart” of a processor—you could say that everything else in the CPU is there to support the ALU.

One of ALU structures • • AE = Arithmetic Extender (Add, Sub, Inc, Dec) LE = Logic Extender (AND, OR, PASS, NOT)

Additional variables for AE & LE • • M: select arithmetic or logic operations – M = 1 ALU will perform arithmetic operation – M = 0 ALU will perform logic operation S 1 & S 0: once arithmetic or logic operations has been selected, these 2 variable will select specific operations to be performed by ALU – M = 1 S 1 & S 0 will select one of Add, Sub, Inc, Dec – M = 0 S 1 & S 0 will select one of AND, OR, PASS, NOT

Arithmetic Extender • Functional Table: • Implementation: LE’s requirement

Logic Extender • Functional Table: • Truth Table: Conforms with AE’s output satisfy AE

Logic Extender (cont. ) • Map & Implementation:

The ALU • • If M = 1, then – Xi = ai, Yi = A(bi), c 0 = S 1 If M = 0, then – Xi = L(ai, bi), Yi = 0, c 0 = 0

ALU function table

ALU’s summary • • This ALU is a good example of hierarchical design. – With the 12 inputs, the truth table would have had 212 = 4096 lines. That’s an awful lot of paper. – Instead, we were able to re-use components that we’ve seen before to construct the entire circuit from a couple of easy-to-understand components. As always, we encapsulate the complete circuit in a “black box” so we can reuse it in fancier circuits.