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Sequential Logic, Slides of Logic

The UCL School of PharmacyLogic

Key to sequential logic: circuit has feedback ... this is an asynchronous sequential circuit. Sequential Logic ... This is a synchronous sequential circuit.

Typology: Slides

2021/2022

Uploaded on 09/27/2022

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Sequential Logic
1
Sequential Logic
๎˜๎˜๎˜‚๎˜ƒ๎˜„๎˜…๎˜†๎˜‡๎˜ˆ๎˜…๎˜‚๎˜†๎˜‡๎˜‰๎˜Š๎˜‰๎˜‚๎˜‹๎˜…๎˜Œ๎˜
๎˜๎˜๎˜‚๎˜ƒ๎˜Ž๎˜๎˜ˆ๎˜๎˜Š๎˜‡๎˜Š๎˜‘๎˜๎˜†๎˜Œ๎˜ˆ๎˜…๎˜‚๎˜†๎˜Š๎˜‡๎˜‰๎˜‰๎˜Š๎˜‡๎˜ˆ๎˜Š๎˜‚๎˜†๎˜๎˜Š๎˜ˆ๎˜…๎˜ƒ๎˜
๎˜๎˜’๎˜‡๎˜“๎˜ˆ๎˜”๎˜๎˜• ๎˜Ž๎˜๎˜†๎˜“๎˜…๎˜–๎˜
๎˜๎˜๎˜—๎˜‹๎˜—๎˜Š๎˜Œ๎˜‚๎˜ƒ๎˜„๎˜…๎˜†๎˜‡๎˜ˆ๎˜…๎˜‚๎˜†๎˜‡๎˜‰๎˜Š๎˜ƒ๎˜๎˜‰๎˜ˆ๎˜…๎˜Ž๎˜‰๎˜…๎˜๎˜˜
๎˜๎˜™ ๎˜๎˜š๎˜๎˜๎˜†๎˜ˆ๎˜…๎˜‡๎˜‰๎˜Š๎˜‰๎˜‚๎˜‹๎˜…๎˜Œ๎˜
๎˜๎˜๎˜‚๎˜ƒ๎˜Ž๎˜๎˜ˆ๎˜๎˜Š๎˜‡๎˜Š๎˜‘๎˜๎˜†๎˜Œ๎˜ˆ๎˜…๎˜‚๎˜†๎˜Š๎˜…๎˜†๎˜Š๎˜‡๎˜Š๎˜“๎˜๎˜˜๎˜…๎˜๎˜“๎˜Š๎˜‚๎˜‘๎˜Š๎˜“๎˜ˆ๎˜๎˜Ž๎˜“
๎˜๎˜™ ๎˜‰๎˜‚๎˜› ๎˜๎˜˜๎˜”๎˜ƒ๎˜‚๎˜˜๎˜๎˜Š๎˜๎˜‘๎˜‘๎˜…๎˜Œ๎˜…๎˜๎˜†๎˜ˆ
๎˜๎˜๎˜—๎˜‹๎˜—๎˜Š๎˜“๎˜œ๎˜…๎˜‘๎˜ˆ๎˜”๎˜‡๎˜๎˜๎˜Š๎˜ƒ๎˜๎˜‰๎˜ˆ๎˜…๎˜Ž๎˜‰๎˜…๎˜๎˜˜
๎˜๎˜ž๎˜๎˜Ÿ๎˜Š ๎˜ˆ๎˜‚๎˜Š๎˜“๎˜๎˜š๎˜๎˜๎˜†๎˜ˆ๎˜…๎˜‡๎˜‰๎˜Š๎˜‰๎˜‚๎˜‹๎˜…๎˜Œ๎˜๎˜Š๎˜Š๎˜Œ๎˜…๎˜˜๎˜Œ๎˜๎˜…๎˜ˆ๎˜Š๎˜œ๎˜‡๎˜“๎˜Š๎˜‘๎˜๎˜๎˜๎˜„๎˜‡๎˜Œ
๎˜! ๎˜“๎˜๎˜Š๎˜ˆ๎˜œ๎˜๎˜Š๎˜˜๎˜๎˜“๎˜๎˜‰๎˜ˆ๎˜Š๎˜‚๎˜‘๎˜Š๎˜‚๎˜†๎˜๎˜Š๎˜“๎˜ˆ๎˜๎˜Ž๎˜Š๎˜‡๎˜“๎˜Š๎˜‡๎˜†๎˜Š๎˜…๎˜†๎˜Ž๎˜๎˜ˆ๎˜Š๎˜ˆ๎˜‚๎˜Š๎˜ˆ๎˜œ๎˜๎˜Š๎˜†๎˜ ๎˜•๎˜ˆ
Sequential Logic
2
๎˜๎˜‚
๎˜๎˜ƒ
๎˜„
๎˜„
๎˜„
๎˜๎˜…
๎˜†๎˜‡๎˜ˆ๎˜‰๎˜Š๎˜…๎˜‹๎˜Œ๎˜Š๎˜‡๎˜…๎˜‹๎˜
๎˜Ž๎˜Š๎˜๎˜Ž๎˜๎˜Š๎˜Œ
๎˜‘๎˜‚
๎˜‘๎˜ƒ
๎˜„
๎˜„
๎˜„
๎˜‘๎˜…
Circuits with feedback
๎˜" ๎˜‚๎˜› ๎˜Š๎˜ˆ๎˜‚๎˜Š๎˜Œ๎˜‚๎˜†๎˜ˆ๎˜˜๎˜‚๎˜‰๎˜Š๎˜‘๎˜๎˜๎˜๎˜„๎˜‡๎˜Œ #
๎˜๎˜› ๎˜œ๎˜‡๎˜ˆ๎˜Š๎˜“๎˜ˆ๎˜‚๎˜Ž๎˜“๎˜Š๎˜–๎˜‡๎˜‰๎˜๎˜๎˜“๎˜Š๎˜‘๎˜˜๎˜‚๎˜ƒ๎˜Š๎˜Œ๎˜Ÿ๎˜Œ๎˜‰๎˜…๎˜†๎˜‹๎˜Š๎˜‡๎˜˜๎˜‚๎˜๎˜†๎˜๎˜Š๎˜๎˜†๎˜๎˜‰๎˜๎˜“๎˜“๎˜‰๎˜Ÿ#
๎˜๎˜ˆ๎˜œ๎˜…๎˜“๎˜Š๎˜…๎˜“๎˜Š๎˜‡๎˜†๎˜Š
๎˜‡๎˜“๎˜Ÿ๎˜†๎˜Œ๎˜œ๎˜˜๎˜‚๎˜†๎˜‚๎˜๎˜“
๎˜“๎˜๎˜š๎˜๎˜๎˜†๎˜ˆ๎˜…๎˜‡๎˜‰๎˜Š๎˜Œ๎˜…๎˜˜๎˜Œ๎˜๎˜…๎˜ˆ
Sequential Logic
3
๎˜’๎˜๎˜“๎˜ˆ๎˜“๎˜ˆ๎˜‰๎˜“๎˜๎˜’
๎˜’๎˜๎˜‡๎˜‹๎˜”๎˜’
๎˜’๎˜”๎˜‹๎˜Œ๎˜‹๎˜’ ๎˜’๎˜•๎˜Œ๎˜‡๎˜๎˜“๎˜”๎˜–๎˜—๎˜‹๎˜๎˜๎˜“๎˜’
๎˜’๎˜˜๎˜’
๎˜’๎˜‚๎˜’
๎˜’๎˜•๎˜Œ๎˜‡๎˜๎˜“๎˜”๎˜–๎˜—๎˜‹๎˜๎˜๎˜“๎˜’
Simplest circuits with feedback: latch
๎˜$๎˜› ๎˜‚๎˜Š๎˜…๎˜†๎˜–๎˜๎˜˜๎˜ˆ๎˜๎˜˜๎˜“๎˜Š๎˜‘๎˜‚๎˜˜๎˜ƒ๎˜Š๎˜‡๎˜Š๎˜“๎˜ˆ๎˜‡๎˜ˆ๎˜…๎˜Œ๎˜Š๎˜ƒ๎˜๎˜ƒ๎˜‚๎˜˜๎˜Ÿ๎˜Š๎˜Œ๎˜๎˜‰๎˜‰
๎˜๎˜› ๎˜…๎˜‰๎˜‰๎˜Š๎˜œ๎˜‚๎˜‰๎˜๎˜Š๎˜–๎˜‡๎˜‰๎˜๎˜๎˜Š๎˜‡๎˜“๎˜Š๎˜‰๎˜‚๎˜†๎˜‹๎˜Š๎˜‡๎˜“๎˜Š๎˜…๎˜ˆ๎˜Š๎˜œ๎˜‡๎˜“๎˜Š๎˜Ž๎˜‚๎˜› ๎˜๎˜˜๎˜Š๎˜‡๎˜Ž๎˜Ž๎˜‰๎˜…๎˜๎˜
๎˜" ๎˜‚๎˜› ๎˜Š๎˜ˆ๎˜‚๎˜Š๎˜‹๎˜๎˜ˆ๎˜Š๎˜‡๎˜Š๎˜†๎˜๎˜› ๎˜Š๎˜–๎˜‡๎˜‰๎˜๎˜๎˜Š๎˜…๎˜†๎˜ˆ๎˜‚๎˜Š๎˜ˆ๎˜œ๎˜๎˜Š๎˜ƒ๎˜๎˜ƒ ๎˜‚๎˜˜๎˜Ÿ๎˜Š๎˜Œ๎˜๎˜‰๎˜‰#
๎˜๎˜“๎˜๎˜‰๎˜๎˜Œ๎˜ˆ๎˜…๎˜–๎˜๎˜‰๎˜Ÿ๎˜Š๎˜„๎˜˜๎˜๎˜‡ ๎˜Š๎˜‘๎˜ ๎˜๎˜๎˜„๎˜‡๎˜Œ ๎˜Š๎˜Ž๎˜‡๎˜ˆ๎˜œ
๎˜๎˜‰๎˜‚๎˜‡๎˜๎˜Š๎˜†๎˜๎˜› ๎˜Š๎˜–๎˜‡๎˜‰๎˜๎˜๎˜Š๎˜…๎˜†๎˜ˆ๎˜‚๎˜Š๎˜Œ๎˜๎˜‰๎˜‰
Sequential Logic
4
Letโ€™s Use This Latch
๎˜% ๎˜œ๎˜‡๎˜ˆ๎˜Š๎˜œ๎˜‡๎˜Ž๎˜Ž๎˜๎˜†๎˜“#
๎˜๎˜‚
๎˜๎˜ƒ
๎˜„
๎˜„
๎˜„
๎˜๎˜…
๎˜†๎˜‡๎˜ˆ๎˜‰๎˜Š๎˜…๎˜‹๎˜Œ๎˜Š๎˜‡๎˜…๎˜‹๎˜
๎˜Ž๎˜Š๎˜๎˜Ž๎˜๎˜Š๎˜Œ
๎˜‘๎˜‚
๎˜‘๎˜ƒ
๎˜„
๎˜„
๎˜„
Sequential Logic
5
What We Need:
๎˜% ๎˜œ๎˜๎˜†๎˜Š๎˜…๎˜†๎˜Ž๎˜๎˜ˆ๎˜“๎˜Š๎˜Œ๎˜œ๎˜‡๎˜†๎˜‹๎˜๎˜—๎˜—๎˜—
๎˜% ๎˜‡๎˜…๎˜ˆ๎˜Š๎˜๎˜†๎˜ˆ๎˜…๎˜‰๎˜Š๎˜Œ๎˜‚๎˜ƒ๎˜„๎˜…๎˜†๎˜‡๎˜ˆ๎˜…๎˜‚๎˜†๎˜‡๎˜‰๎˜Š๎˜‰๎˜‚๎˜‹๎˜…๎˜Œ๎˜Š๎˜œ๎˜‡๎˜“๎˜Š๎˜‘๎˜…๎˜†๎˜…๎˜“๎˜œ๎˜๎˜๎˜Š๎˜‡๎˜†๎˜๎˜Š๎˜˜๎˜๎˜“๎˜๎˜‰๎˜ˆ๎˜Š๎˜…๎˜ˆ๎˜Š๎˜“๎˜ˆ๎˜‡๎˜„๎˜‰๎˜๎˜—๎˜—๎˜—
๎˜$๎˜œ๎˜๎˜†๎˜Š๎˜“๎˜‡๎˜ƒ๎˜Ž๎˜‰๎˜๎˜Š๎˜ˆ๎˜œ๎˜๎˜Š๎˜‚๎˜๎˜ˆ๎˜Ž๎˜๎˜ˆ๎˜Š๎˜–๎˜‡๎˜‰๎˜๎˜ ๎˜Š๎˜‡๎˜†๎˜๎˜Š๎˜“๎˜‡๎˜–๎˜๎˜—๎˜—๎˜—
๎˜๎˜’๎˜๎˜ ๎˜๎˜Š๎˜ˆ๎˜œ๎˜๎˜Š๎˜“๎˜‡๎˜–๎˜๎˜ ๎˜Š๎˜‚๎˜๎˜ˆ๎˜Ž๎˜๎˜ˆ๎˜Š๎˜„๎˜‡๎˜Œ ๎˜Š๎˜ˆ๎˜‚๎˜Š๎˜ˆ๎˜œ๎˜๎˜Š๎˜…๎˜†๎˜Ž๎˜๎˜ˆ๎˜Š๎˜‚๎˜‘๎˜Š๎˜ˆ๎˜œ๎˜๎˜Š๎˜Œ๎˜‚๎˜ƒ๎˜„๎˜…๎˜†๎˜‡๎˜ˆ๎˜…๎˜‚๎˜†๎˜‡๎˜‰๎˜Š๎˜‰๎˜‚๎˜‹๎˜…๎˜Œ
๎˜& ๎˜‡ ๎˜๎˜Š๎˜“๎˜๎˜˜๎˜๎˜Š๎˜ˆ๎˜œ๎˜๎˜Š๎˜“๎˜‡๎˜–๎˜๎˜๎˜Š๎˜‚๎˜๎˜ˆ๎˜Ž๎˜๎˜ˆ๎˜Š๎˜Œ๎˜‡๎˜†'๎˜ˆ๎˜Š๎˜Œ๎˜œ๎˜‡๎˜†๎˜‹๎˜
๎˜๎˜ž๎˜๎˜Ÿ๎˜Š ๎˜…๎˜๎˜๎˜‡๎˜๎˜Š๎˜› ๎˜๎˜Š๎˜“๎˜‡๎˜ƒ๎˜Ž๎˜‰๎˜๎˜Š๎˜ˆ๎˜œ๎˜ ๎˜Š๎˜˜๎˜๎˜“๎˜๎˜‰๎˜ˆ๎˜Š๎˜‡๎˜ˆ๎˜Š๎˜ˆ๎˜œ๎˜๎˜Š๎˜˜๎˜…๎˜‹๎˜œ๎˜ˆ๎˜Š๎˜ˆ๎˜…๎˜ƒ๎˜(๎˜Š๎˜…๎˜—๎˜๎˜—๎˜Š๎˜› ๎˜œ๎˜ ๎˜†๎˜Š๎˜…๎˜ˆ๎˜Š๎˜…๎˜“๎˜Š๎˜˜๎˜๎˜‡๎˜๎˜Ÿ
๎˜) ๎˜†๎˜‰๎˜Ÿ๎˜Š๎˜ˆ๎˜œ๎˜๎˜†๎˜Š๎˜ ๎˜‚๎˜Š๎˜› ๎˜๎˜Š๎˜๎˜Ž๎˜๎˜‡๎˜ˆ ๎˜๎˜Š๎˜ˆ๎˜œ๎˜๎˜Š๎˜“๎˜ˆ๎˜‚๎˜˜๎˜๎˜๎˜Š๎˜–๎˜‡๎˜‰๎˜๎˜
๎˜
" ๎˜‚๎˜› ๎˜Š๎˜๎˜‚๎˜Š๎˜› ๎˜๎˜Š ๎˜†๎˜‚๎˜›๎˜Š๎˜› ๎˜œ๎˜๎˜†๎˜Š๎˜ˆ๎˜‚๎˜Š๎˜“๎˜‡๎˜ƒ๎˜Ž๎˜‰๎˜ #
๎˜
" ๎˜‚๎˜› ๎˜Š๎˜๎˜‚๎˜Š๎˜› ๎˜๎˜Š ๎˜†๎˜‚๎˜›๎˜Š๎˜› ๎˜œ๎˜๎˜†๎˜Š๎˜ˆ๎˜œ๎˜๎˜Š๎˜…๎˜†๎˜Ž ๎˜๎˜ˆ๎˜“๎˜Š๎˜Œ๎˜œ๎˜‡๎˜†๎˜‹๎˜๎˜#
๎˜
" ๎˜‚๎˜› ๎˜Š๎˜๎˜‚๎˜Š๎˜› ๎˜๎˜Š ๎˜†๎˜‚๎˜›๎˜Š๎˜œ๎˜‚๎˜› ๎˜Š๎˜‰๎˜‚๎˜†๎˜‹๎˜Š๎˜ˆ๎˜‚๎˜Š๎˜› ๎˜‡๎˜…๎˜ˆ#
Sequential Logic
6
What We Need:
๎˜* ๎˜Š๎˜Œ๎˜…๎˜˜๎˜Œ๎˜๎˜…๎˜ˆ๎˜Š๎˜ˆ๎˜œ๎˜‡๎˜ˆ๎˜Š๎˜Œ๎˜‡๎˜†๎˜Š
๎˜“๎˜‡๎˜ƒ๎˜Ž๎˜‰๎˜
๎˜‡๎˜Š๎˜–๎˜‡๎˜‰๎˜๎˜
๎˜* ๎˜Š๎˜“๎˜…๎˜‹๎˜†๎˜‡๎˜‰๎˜Š๎˜ˆ๎˜œ๎˜‡๎˜ˆ๎˜Š๎˜“๎˜‡๎˜Ÿ๎˜“๎˜Š
๎˜› ๎˜œ๎˜๎˜†
๎˜ˆ๎˜‚๎˜Š๎˜“๎˜‡๎˜ƒ๎˜Ž๎˜‰๎˜
๎˜+๎˜ ๎˜‹๎˜,๎˜ˆ๎˜˜๎˜…๎˜‹๎˜‹๎˜๎˜˜๎˜๎˜๎˜Š- ๎˜Š๎˜‘๎˜‰๎˜…๎˜Ž,๎˜‘๎˜‰๎˜‚๎˜Ž๎˜Š.๎˜˜๎˜๎˜‹๎˜…๎˜“๎˜ˆ๎˜๎˜˜/
๎˜๎˜™ ๎˜‡๎˜ƒ๎˜Ž๎˜‰๎˜๎˜“๎˜Š๎˜‚๎˜†๎˜Š๎˜Ž๎˜‚๎˜“๎˜…๎˜ˆ๎˜…๎˜–๎˜๎˜Š๎˜๎˜๎˜‹๎˜ ๎˜Š๎˜‚๎˜‘๎˜Š๎˜Œ๎˜‰๎˜‚๎˜Œ
๎˜" ๎˜‚๎˜‰๎˜๎˜“๎˜Š๎˜–๎˜‡๎˜‰๎˜๎˜๎˜Š๎˜๎˜†๎˜ˆ๎˜…๎˜‰๎˜Š๎˜†๎˜๎˜• ๎˜ˆ๎˜Š๎˜Ž๎˜‚๎˜“๎˜…๎˜ˆ๎˜…๎˜–๎˜๎˜Š๎˜๎˜๎˜‹๎˜
๎˜& ๎˜‚๎˜“๎˜ˆ๎˜Š๎˜Œ๎˜‚๎˜ƒ๎˜ƒ๎˜‚๎˜†๎˜Š๎˜“๎˜ˆ๎˜‚๎˜˜๎˜‡๎˜‹๎˜๎˜Š๎˜๎˜‰๎˜๎˜ƒ๎˜๎˜†๎˜ˆ
๎˜๎˜๎˜‰๎˜‚๎˜Œ
๎˜0๎˜๎˜˜๎˜…๎˜‚๎˜๎˜…๎˜Œ๎˜Š๎˜“๎˜…๎˜‹๎˜†๎˜‡๎˜‰(๎˜Š๎˜๎˜‡๎˜Œ๎˜œ๎˜Š๎˜˜๎˜…๎˜“๎˜…๎˜†๎˜‹๎˜Š๎˜๎˜๎˜‹๎˜๎˜Š๎˜“๎˜…๎˜‹๎˜†๎˜‡๎˜‰๎˜“๎˜Š- ๎˜Š๎˜‘๎˜‰๎˜…๎˜Ž,๎˜‘๎˜‰๎˜‚๎˜Ž๎˜“๎˜Š๎˜ˆ๎˜‚๎˜Š๎˜“๎˜‡๎˜ƒ๎˜Ž๎˜‰๎˜
๎˜* ๎˜‰๎˜‰๎˜Š๎˜˜๎˜๎˜‹๎˜…๎˜“๎˜ˆ๎˜๎˜˜๎˜“๎˜Š๎˜“๎˜‡๎˜ƒ๎˜Ž๎˜‰๎˜๎˜Š๎˜‡๎˜ˆ๎˜Š๎˜ˆ๎˜œ๎˜๎˜Š๎˜“๎˜‡๎˜ƒ๎˜๎˜Š๎˜ˆ๎˜…๎˜ƒ๎˜
๎˜ ๎˜‚
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Sequential Logic 1

Sequential Logic

Sequential Logic 2

   

Circuits with feedback

Sequential Logic 3

Simplest circuits with feedback: latch

Sequential Logic 4

Letโ€™s Use This Latch

   

What We Need:

What We Need:

 

Sequential Logic 7

Letโ€™s Use This D flip-flop

   

 

Sequential Logic 8



 

  

     

Registers



      ^ 

Sequential Logic 9

Example - Circuit with Feedback

Sequential Logic 10

Examples (contโ€™d)

Example - Circuit without Feedback

        



 

  





 

Timing Methodologies (contโ€™d)



     

Binary counter

+,^ '^ *^ ' *^ '^ *^ ' *

Other Counters: cheaper/faster