🚀 Digital Logic GATE & NTA UGC NET CSE | Part 11 : Subtractor Circuits & Multiplexer | Combinational
Автор: NTA UGC NET Computer Science CSE
Загружено: 2025-06-12
Просмотров: 43
Dive into subtractor design and get an introductory look at multiplexers in Part 11 of our Digital Logic series for GATE & NTA UGC NET CSE. First, we recap half subtractors, derive difference & borrow equations, and show NAND-gate realizations. Then we extend to full subtractors, explore Boolean simplification (including alternate standard forms), and demonstrate implementation via two half-subtractor blocks plus a gate. Finally, we introduce the 2×1 and 4×1 multiplexer (data selector), learn how select lines route inputs, and derive canonical output expressions in SOP form. Perfect for mastering key combinational building blocks!
Timestamps
00:00 – Intro & Recap of Adders → Subtractor Transition
00:00:52 – Half Subtractor: Difference & Borrow Definitions
00:02:13 – Binary Borrow Concept via “2 – 1 = 1”
00:03:20 – Difference = A ⊕ B; Borrow = A̅·B
00:03:54 – NAND-Gate Realization of Half Subtractor
00:07:29 – Full Subtractor Truth-Table Walkthrough
00:08:24 – Deriving Full Subtractor Difference (A⊕B⊕C)
00:10:37 – Full Subtractor Borrow Equations & Standard Form
00:12:27 – Alternate Borrow Expression & Simplification
00:14:34 – NAND-Gate Implementation of Full Subtractor (9 NANDs)
00:24:43 – Full Subtractor via Two Half-Subtractors + Gate
00:28:26 – Why Adders Matter More than Subtractors in Practice
00:29:31 – Multiplexer Intro: Definition & Data-Selector Role
00:31:29 – Select Lines: Counting & Logic (2-to-1 MUX)
00:33:24 – SOP Expression for 2×1 MUX: S̅·I₀ + S·I₁
00:37:41 – 4×1 MUX Example: s₁s₀ → i₀…i₃ Routing
00:38:56 – SOP Expression for 4×1 MUX: S₁̅S₀̅I₀ + … + S₁S₀I₃
00:40:31 – Practice Question: MUX + NOT Example & Boolean Reduction
00:45:44 – Key Takeaways & Next Topic Preview (Multiplexer Depth)
▶️ Why Watch?
• Master subtractor circuits: half vs full, borrow logic, SOP forms
• Learn NAND-only implementations for hardware cost reduction
• Understand MUX as parallel-to-serial converter & data selector
• Derive general MUX expressions for any N-to-1 routing
• Ideal revision for GATE Digital Logic & UGC NET CSE
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