Related Concepts: 5.01 Sequential Logic Fundamentals, Latches & Flip-Flops (SR & JK) | 5.02 Flip-Flop Variants (Master-Slave JK, T & D Flip-Flops) & Triggering Mechanics | 5.04 Synchronous Sequential Circuit Analysis & Synthesis

5.03 Flip-Flop Conversions & Functional Transformation Mechanics

Conversion questions, all 10–13 marks

Question	Years	Marks
Convert an S-R flip-flop to a J-K flip-flop	2017, 2018	10
Convert a J-K flip-flop to an S-R flip-flop	2024	12
Show that tying the two external JK inputs together forms a D flip-flop (part iv of the 2024 tables question)	2024	part of 13
”JK flip-flop is the refinement of RS flip-flop” — justify	2023 (11), 2025 (09)	9–11

All four reduce to the same 4-step algorithm in §1: required excitation → available excitation → K-map → conversion logic.

Overview: Flip-flop conversion is the process of synthesizing combinational drive logic to convert an available Source Flip-Flop into a desired Target Flip-Flop. This systematic design technique allows any flip-flop type (SR, JK, D, or T) to emulate the operational characteristics of any other flip-flop type.

1. The Systematic 4-Step Conversion Algorithm

The conversion process follows a structured methodology: construct a combined conversion table, append source flip-flop excitation requirements, derive drive logic via K-Maps, and finally draw the logic diagram.

2. SR-to-JK Flip-Flop Conversion

Exam Problem (PYQ 2017, 2018 — 10 marks)

Question (verbatim): Convert an S-R flip-flop to a J-K flip-flop.

• Available (Source) FF: SR Flip-Flop

• Desired (Target) FF: JK Flip-Flop

2.1 Conversion Table

Target Inputs (J, K)	Present State (Qn)	Next State (Qn+1)	Source SR Excitation (S, R)
0 0	0	0	0 X
0 0	1	1	X 0
0 1	0	0	0 X
0 1	1	0	0 1
1 0	0	1	1 0
1 0	1	1	X 0
1 1	0	1	1 0
1 1	1	0	0 1

2.2 K-Map Optimization for Drive Inputs S and R

1. For Input S(J, K, Qn): Grouping minterm m4 (100) and m6 (110) yields: S = J · Qn’

2. For Input R(J, K, Qn): Grouping minterm m3 (011) and m7 (111) yields: R = K · Qn

2.3 Synthesized Circuit Schematic

The SR flip-flop is driven by two 2-input AND gates where J is ANDed with Q’ to drive S, and K is ANDed with Q to drive R.

3. JK-to-SR Flip-Flop Conversion

Exam Problem (PYQ 2024 — 12 marks)

Question (verbatim): Convert a J-K flip-flop to a S-R flip-flop.

This is the reverse of §2 and the answer is different — do not simply reuse the SR→JK result. Note also that $S=R=1$ is forbidden in SR, so those rows become don’t cares in the K-maps.

• Available (Source) FF: JK Flip-Flop

• Desired (Target) FF: SR Flip-Flop

3.1 Conversion Table

Target Inputs (S, R)	Present State (Qn)	Next State (Qn+1)	Source JK Excitation (J, K)
0 0	0	0	0 X
0 0	1	1	X 0
0 1	0	0	0 X
0 1	1	0	X 1
1 0	0	1	1 X
1 0	1	1	X 0
1 1	0	X	X X
1 1	1	X	X X

3.2 Drive Logic Equations

From K-map simplification: J = S and K = R.

Practical Insight: Since J = S and K = R, connecting S directly to J and R directly to K transforms a JK flip-flop into an SR flip-flop without requiring any external logic gates!

4. JK-to-D & JK-to-T Conversions

Exam Problem (PYQ 2024 — part iv of a 13-mark question)

Question (verbatim): …(iv) Show that tying the two external inputs together forms a D flip-flop.

Careful — the standard result differs. Tying $J$ and $K$ directly together ($J=K=T$) gives a T (toggle) flip-flop. To obtain a D flip-flop you tie $J=D$ and $K=D^{\prime }$ — i.e. connected through an inverter. Show both and state which the question means; if the paper says “tied together” and asks for D, note the inverter explicitly.

4.1 Converting JK to D Flip-Flop

Goal: Force J = D and K = D’. Drive Equations: J = D and K = D’. Implementation: Pass D directly to J, and pass D through a NOT gate to K.

4.2 Converting JK to T Flip-Flop

Goal: Force J = T and K = T. Drive Equations: J = T and K = T. Implementation: Tie J and K together and connect them to a common input signal T.

5. Master Summary Table of Conversion Equations

Source FF	Target FF	Drive Logic Equations
SR	JK	S = J·Qn’, R = K·Qn
SR	D	S = D, R = D’
SR	T	S = T·Qn’, R = T·Qn
JK	SR	J = S, K = R
JK	D	J = D, K = D’
JK	T	J = T, K = T
D	T	D = T ⊕ Qn = T·Qn’ + T’·Qn
T	D	T = D ⊕ Qn = D·Qn’ + D’·Qn

6. Past Year Master Questions & Solutions

PYQ Master Problem (2017, 2018): SR to JK Conversion

Question: Convert an S-R flip-flop to a J-K flip-flop. Show all conversion tables, K-maps, and final logic diagrams. [8 Marks]

Solution:

1. Conversion Table Construction: Construct the 8-row table mapping target J,K and Qn to source S,R excitations (Section 2.1).

2. K-Map Derivation: Show 3-variable K-maps for S and R: S(J,K,Qn) = J·Qn’ and R(J,K,Qn) = K·Qn.

3. Circuit Diagram: Draw the SR flip-flop driven by two 2-input AND gates (Section 2.3).