ch 4. combinational logic design principles
DESCRIPTION
Ch 4. Combinational Logic Design Principles. Combinational Logic Circuit Outputs depend only on its current inputs No feedback loop. Sequential Logic Circuit Outputs depend on its current inputs and present states F eedback loop. 4.1 Switching Algebra. ‘+’ : ‘OR’. ‘ ’ : ‘AND’. - PowerPoint PPT PresentationTRANSCRIPT
Ch 4. Combinational Logic Design Principles
• Combinational Logic Circuit– Outputs depend only on its current inputs– No feedback loop
• Sequential Logic Circuit– Outputs depend on its current inputs and present states– Feedback loop
4.1 Switching Algebra
‘+’ : ‘OR’
‘’ : ‘AND’
& are obvious (by perfect induction)
is identical to the distributive law for integers and reals
Switching-algebra theorems
NAND
DeMorgan’s Th.
NOR
DeMorgan’s Th.
Black box Representation with Truth table
Active Low
Active Low
Black box Representation with Truth table
DualityPositive Negative 𝑭 (𝑿𝟏 ,𝑿𝟐 ,… 𝑿𝒏 )⇒ 𝑭 𝑫 (𝑿𝟏
′ , 𝑿𝟐′ ,…𝑿𝒏′ )
𝑭 (𝑿𝟏 ,𝑿𝟐 ,… 𝑿𝒏 )=[𝑭 𝑫 (𝑿𝟏′ ,𝑿𝟐
′ ,…𝑿𝒏′ ) ]′
[𝑭 (𝑿𝟏 ,𝑿𝟐 ,…𝑿𝒏 ) ]′=[𝑭 𝑫 (𝑿𝟏′ , 𝑿𝟐
′ ,… 𝑿𝒏′ ) ]❑
→𝑮𝒆𝒏𝒆𝒓𝒂𝒍𝒊𝒛𝒆𝒅 𝑫𝒆𝑴𝒐𝒓𝒈𝒂𝒏′ 𝒔𝑻𝒉 .
𝑫𝒖𝒂𝒍𝒊𝒕𝒚
Function with 3 inputX, Y, Z
𝑭 (𝑿 ,𝒀 ,𝒁 )
𝑪𝒂𝒏𝒐𝒏𝒊𝒄𝒂𝒍 𝑺𝒖𝒎−𝑨𝒔𝒖𝒎𝒐𝒇 𝒎𝒊𝒏𝒕𝒆𝒓𝒎𝒔 𝒕𝒐𝒑𝒓𝒐𝒅𝒖𝒄𝒆𝒐𝒖𝒕𝒑𝒖𝒕𝒔 ′ 𝟏 ′
DeMorgan’s Th.
4.2 Combinational-Circuit Analysis
F(X, Y, Z)
F(X, Y, Z)
¿ 𝑿𝒁+𝒀 ′ 𝒁+𝑿 ′𝒀𝒁 ′
Three-level without considering inverter
(𝑽 ∙𝑾 ∙𝐗 )+ (𝐘 ∙𝒁 )=(𝑽 +𝒀 ) ∙ (𝑽 +𝒁 ) ∙ (𝑾 +𝒀 ) ∙(𝑾 +𝒁 )∙(𝑿+𝒀 ) ∙(𝑿+𝒁 )
“Add-out” to obtain a product of sums by T8’
T8’
Sum of products
Product of sums
(Figure 4-12)
(Figure 4-13)
Same
4.3 Combinational-Circuit Synthesis
Prime number detector
¿𝑷𝒂𝒏𝒊𝒄+𝑬𝒏𝒂𝒃𝒍𝒆 ∙𝑬𝒙𝒊𝒕𝒊𝒏𝒈 ′ ∙𝑺𝒆𝒄𝒖𝒓𝒆 ′
𝒏𝒐𝒏𝒔𝒕𝒂𝒏𝒅𝒂𝒓𝒅𝒈𝒂𝒕𝒆
𝒆𝒍𝒎𝒊𝒏𝒂𝒕𝒆𝒔 𝒏𝒐𝒏𝒔𝒕𝒂𝒏𝒅𝒂𝒓𝒅𝒈𝒂𝒕𝒆
NAND
NOR
𝐹= ∑𝑁3𝑁2𝑁1𝑁0
❑
(1,3,5,7,2,11,13 )
𝑮𝒓𝒂𝒚 𝑺𝒆𝒒𝒖𝒆𝒏𝒄𝒆
𝑴𝒊𝒏𝒕𝒆𝒓𝒎𝑮𝒓𝒂𝒚 𝑺𝒆𝒒𝒖𝒆𝒏𝒄𝒆
𝒅𝒊𝒔𝒕𝒊𝒏𝒈𝒖𝒊𝒔𝒉𝒆𝒅𝟏−𝒄𝒆𝒍𝒍𝒔
𝑬𝑷𝑰
𝑬𝑷𝑰
4.4 Timing Hazards
𝑿𝒁𝑷=𝟏𝑿=𝟏
𝐘 𝒁=𝟎
Unwanted Output
Static-1 Hazard : Momentary output ‘0’ to occur during a transition in the differing input variable
Static-0 Hazard : Momentary output ‘1’ to occur during a transition in the differing input variable
Unwanted Output
𝑻𝒐𝒆𝒍𝒊𝒎𝒊𝒏𝒂𝒕𝒆 𝒔𝒕𝒂𝒕𝒊𝒄𝟏−𝒉𝒂𝒛𝒂𝒓𝒅