Flip-Flop Conversion Equations: JK, SR, D, and T

This page provides flip-flop (FF) conversion equations for various transformations between JK, SR, D, and T flip-flop types. These equations are invaluable when you need to implement a specific flip-flop behavior using a different type of flip-flop that’s readily available or more suitable for your design.

Flip-Flop Conversion Equations

Here’s a breakdown of the conversion equations, covering all the common flip-flop transformations:

SR FF to JK FF Conversion

• S = J * Qn’ (S equals J ANDed with Qn’)
• R = K * Qn (R equals K ANDed with Qn)

SR FF to D FF Conversion

• S = D
• R = D’ (R equals the complement of D)

SR FF to T FF Conversion

• S = T * Qn’ (S equals T ANDed with Qn’)
• R = T * Qn (R equals T ANDed with Qn)

JK FF to SR FF Conversion

• J = S
• K = R

JK FF to D FF Conversion

• J = D
• K = D’ (K equals the complement of D)

JK FF to T FF Conversion

• J = T
• K = T

D FF to SR FF Conversion

• D = S + R’ * Qn (D equals S ORed with the result of R’ ANDed with Qn)

D FF to JK FF Conversion

• D = J * Qn’ + K’ * Qn (D equals (J ANDed with Qn’) ORed with (K’ ANDed with Qn))

D FF to T FF Conversion

• D = T XOR Qn (D equals T exclusive-ORed with Qn)

T FF to JK FF Conversion

• T = J * Qn’ + K * Qn (T equals (J ANDed with Qn’) ORed with (K ANDed with Qn))

T FF to SR FF Conversion

• T = S * Qn’ + R * Qn (T equals (S ANDed with Qn’) ORed with (R ANDed with Qn))

T FF to D FF Conversion

• T = D XOR Qn (T equals D exclusive-ORed with Qn)

Usage

The flip-flop conversion equations listed above provide a means to describe the input signals required for a “source” flip-flop type to behave like a “target” flip-flop type. This is crucial for designing digital circuits where you may want to use readily available flip-flop types to emulate the functionality of a more specialized or desired type. By applying these equations, one can translate the desired behavior into the necessary input signals for the available hardware.