Lecture 4

Lecture 4 - Th The University of Texas at Dallas Erik...

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
Erik Jonsson School of Engineering and h U i it f T t D ll Computer Science The University of Texas at Dallas Exclusive OR/Exclusive NOR (XOR/XNOR) XOR and XNOR are useful logic functions. Both have two or more inputs . The truth table for two inputs is shown at right. XOR/XNOR Truth Table a b a XOR b a XNOR b 00 0 1 aXORb = 1 if and only if (iff) a b . a XNOR b = 1 if and only if (iff) a = b . Both may also have many inputs. For >2 01 1 0 10 1 0 inputs, the XOR output is 1 for an odd number of 1 inputs; XNOR has a 1 output for an even number of 1 inputs . ymbols are shown below and to the right 1 1 0 1 XNOR = (ab+ab) Symbols are shown below and to the right. a b a b XOR Like NAND and NOR, XOR and XNOR are not asic Boolean functions, © N. B. Dodge 09/09 1 Lecture #4: More Complex Combinational Logic Circuits a b a b XNOR XOR = ab+ab basic Boolean functions, but can be made from AND , OR and NOT.
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Erik Jonsson School of Engineering and h U i it f T t D ll Computer Science The University of Texas at Dallas More Boolean Expressions and Circuits Let us look at a few more Boolean expressions and the circuits that result. Consider the following SOP expression gp and truth table: f = abc+abc+abc: a b c f 0 0 0 0 a 0 0 1 0 0 1 0 0 0 1 1 0 1 0 0 0 b c f 1 0 1 1 1 1 0 1 1 1 1 1 he circuit is shown at right. © N. B. Dodge 09/09 2 Lecture #4: More Complex Combinational Logic Circuits The circuit is shown at right. Can this circuit be simplified?
Background image of page 2
Erik Jonsson School of Engineering and h U i it f T t D ll Computer Science The University of Texas at Dallas Simplifying the Circuit The circuit is simplifiable. Thus: f = abc+abc+abc = abc+abc+abc+abc , = (abc+abc)+(abc+abc) = ab(c+c)+ac(b+b) . a () ()( ) We got the blue result using the identity x+x = x (thus abc = abc + abc). Grouping the expressions (turquoise), we then factor b c f riginal Circuit terms, remembering that xy + xz = x(y + z) to get the red expression. Note that all the expressions are equivalent . ow in the red expression we know that Original Circuit b Now, in the red expression, we know that the items in parentheses = 1 (x+x = 1). Thus f = ab + ac . he original and simplified circuits are implified Circuit f a c © N. B. Dodge 09/09 3 Lecture #4: More Complex Combinational Logic Circuits The original and simplified circuits are shown at right. Simplified Circuit
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Erik Jonsson School of Engineering and h U i it f T t D ll Computer Science The University of Texas at Dallas Deriving the Expression from the Circuit Sometimes we may develop an experimental circuit to perform a function, and then want to simplify it. i lif th i it il d To simplify the circuit easily, we need the Boolean expression for that circuit . We can then simplify the logic design using that expression. he circuit at right is an example: The Boolean expression is: Top gate: Output = ab.
Background image of page 4
Image of page 5
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 35

Lecture 4 - Th The University of Texas at Dallas Erik...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online