 Open Access
 Total Downloads : 5
 Authors : Ogunlere Samson, Ajaegbu Chigozirim, Kanu Richmond, Somefun Olawale
 Paper ID : IJERTV8IS010077
 Volume & Issue : Volume 08, Issue 01 (January – 2019)
 Published (First Online): 03022019
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Implementation of an Alternative High Performance Flip Flop to JK Flip Flop
1Ogunlere Samson, 2Ajaegbu Chigozirim, 3Kanu Richmond, 4Somefun Olawale
1234Computer Science Department, Babcock University, IlishanRemo, Nigeria
Abstract
– Computer performance is primarily affected by the processor and memory. If either one reaches its limits, the performance of the whole system degrades. As semiconductor technology advances, the performance gap between processor and memory has become one of the major issues in computer design. This situation causes a growing gap between processor and memory in the performance. Hence the design of an efficient and high performance memory element known as FlipFlop Extension is of crucial importance in computer design. The analysis of the existing structures is necessary when the requirement of the FlipFlop is for lowpower and high speed digital applications. This study is dedicated to the investigation of the existing conventional memory elements, the SET /RESET (SR) and JUMPKEY (JK) Flip Flops
performance and the result is used to evaluate the design of an alternative Flip Flop known as Flip Flop Extension. It is evidence from the analysis, that the JKFF Extension at 87.5% has one gate less than the conventional SR & JKFFs. This is a great advantage in performance because fewer gates enhance performance in which numbers of gate/ transistors represent hardware cost.
Key Words: Conventional Flip Flop, Flip Flop Extension, Boolean Equation, KMap, DeMorgans Theorem.

INTRODUCTION
FlipFlops are digital circuits with two stable, self maintaining states that are used as storage/ memory elements such as Random Access Memory (RAM), Caches Memory and Read Only Memory (ROM). They are also very useful in the following electronic digital devices design; Sequence Detector, Data Synchronizer, Frequency Divider, Registers (data transfer), Counters and Registers in Central Processing Unit (CPU) for data transfer. They are derived from Sequential Logic Circuits which are the main electronics circuits that make the development of computers possible. The ability of computer systems to operate without the continuous human intervention is solely achieved through sequential logic circuits, the building blocks of Flip Flops [1].

MOTIVATION FOR THE STUDY
It has been observed that computer performance is primarily affected by the processor and memory. If either one reaches its limits (which may initially be the memory), the performance of the whole system degrades. As semiconductor technology advances, the performance gap between processor – the Central Processing Unit (CPU) and main memory – the Random Access Memory (RAM) has become one of the major issues in computer design. In the
past 45 years, an exponential rate of improvement has been witnessed in semiconductor technology. The processor performance increases at a rate of 60% per year while the memory performance increases just 10% per year [2; 3]. This situation causes a 50% growing gap between processor and memory in the performance as depicted in Figure 1.1. If memory fails to keep pace with the processors constant demands, the processor stalls in a wait state, and valuable processing time is lost. This imbalance has become one major bottleneck in further improving the computer performance.
One reason memory system performance has consistently lagged processor performance is that memory systems typically consist of one or more chips that are designed and manufactured separately from the processor, and the performance of the interconnected multichip memory system is difficult to scale to achieve higher datarate and lower access latency. Memory system datarates are increasing with each new generation of memory devices at the rate of 100% every three years, and memory row cycle times are decreasing at a rate of approximately 7% per year [4]. The collective trends are increasing the ratio of row cycle times to the duration of data bursts on the data bus. This is why it is imperative to critically evaluate the existing conventional JKFF and the need to bridge the speed gap between memory and processor by enhancing the memory speed through logical modification frameworks of the conventional JKFF which utilizes 75% out of the 100% of its states.
Figure 1.1: Processor and DRAM Memory Gap [2; 3]

DESIGNING SR AND JKFLIP FLOPS
We start by designing JKFF from first principle Set and Reset Flip Flop (SRFF) using NOR and NAND gate Configurations. When the forbidden states of an SRFlip Flop (as shown in Table 1.1) are converted to toggling states,
a JKFlip Flop is so obtained. Hence, such a JKFlip Flop retains the rest features of an SRFlip Flop, such as its resting and active states; thus making a JKFlip Flop to attain 75% active states utilization as against 50% active states utilization of an SRFlip Flop on conversion of SRFF to JK FF. The remaining 25% rest state of SRFF is being examined in this study.
3.1. Design Logic Circuit of an SRFlip Flop
The Truth Table of Table 1.1 is converted into a KMap in order to obtain the minimized logic equations of the SRFlip Flop as depicted in Table 1.2.
Logic equations (1a, 1b) & (1.1a, 1.2b) are derived from the KMap and they can be used to construct the Flip Flop using the different gates as given by the equations. However, it is customary to use NOR and NAND gates to construct logic equations (1a, 1b) and (1.1a, 1.2b) respectively by converting the equations into these gates. The mathematical analysis of these equations as ascertained in [12] & [13] is as follows:
Fig. 1.2(b): SR NAND gates Flip Flop Equation Omotosho & Ogunlere (2013)

PROPOSED FLIP FLOP EXTENSION
Possibilities of alternative Flip Flops, to conventional JK Flip Flop are proposed. These different JKFlip Flops are tagged as highlighted in Table 1.2, and are stated according to our adopted convention as follows:
Table 1.2: Proposed Flip Flop Extension Concept
+ = + ()
= + (1)
Put equation (1c) into (1a), we have
+1 = + + (1)
Complement equation (1d), we have
Option 1: 87.5% utilization Flip Flops identified as JK FF Extension 0; (for Rest 1 0); One state at rest.
+ +
+ +
+ =
()
Option 2: 87.5% utilization Flip Flops identified as
JK
+ = + ()
= + (1)
FF Extension 1; (for Rest 0 1); One state at rest.
Put equations (1f) into (1b), we have
+1 = + + (1)
Complement equation (1g), we have
+ = + + () Combining equations (1e) and (1h) results in the construction of SRFF Logic Circuit Diagram using only NOR gates as shown in Figure 1.2(a). Similarly the same procedure is followed to obtain the logic circuit diagram of SRFF using NAND Gates as shown in Figure 1.2(b).
Fig. 1.2(a): SR NOR gates Flip Flop Equation Omotosho & Ogunlere (2013)
Option 3: 100% utilization Flip Flops identified as XY FF – No Rest States.
The Truth Table of these possible options to conventional JKFlip Flop tagged JKFF Extensions is presented in Tables 1.3 and 1.4 with reference to Conventional JKFF from where their simplified Boolean equations are derived.
Q
n +1
Substitute equations (2.2b) & (2.2c) into equation (2.2), we have

MATHEMATICAL ANALYSIS OF JKFF DESIGN
The conversion of SRFF to JKFF as a Positive Logic Design is mathematically analyzed as follows using DeMorgans theorem, Boolean algebra rules and KMap technique.
5.1 JK000, 001 Rest: Conventional JK Flip Flop at 75% active states utilization
From Kmap on JK Flip Flop at 75% active states utilization, the simplified equation of 2.1 is derived using NOR gate configuration as Positive Logic design.
+1 = + (2.1)
NAND GATES (1, 2, 3)
+1 = + + + (2.2)
+ + +
+ + +
+ = (. )
Combining equations (2.1a) and (2.2a) will produce NAND gate configuration of Figure 1.2a. Combining equations (2.1e) and (2.2e) will produce NOR gate configuration of Figure 1.2b.
Figure 1.2 (a): Logic Circuit of Conventional JKFlip Flop – 75% (NAND Gate Configuration.)
Therefore, equations (2.1e) & (2.2e) can be combined as presented in Figure 1.2b
+ = + =
(. )
NOR GATES (1, 2, 3)
.
Figure 1.2 (b): Logic Circuit of Conventional JKFlip Flop – 75% (NOR Gate Configuration)
= + (2.1)
Note that the positive logic design configuration is actually
= + (2.1)
the complement of the negative logic design configuration;
Substitute equations (2.1b) & (2.1c) into equation (2.1), we have
= + + + (2.1)
which shows that either design will produce the same performance.

USING CHARACTERISTIC EQUATIONS TO SIMPLIFIED JKFLIP FLOP DESIGN
+1
+ + +
+ + +
+ = (. )
+1 = + (2.2)
NAND GATES (4, 5, 6)
The complete Logic Circuit Diagrams based on the Kmap analysis and the characteristic equations derived from the state diagram Excitation Table are constructed in Figures 1.2(c) and 1.2(d) respectively. These two circuit diagrams perform the same memory element functions.
+ = + =
. . (. )
NOR GATES (4, 5, 6)
.
= + (2.2)
Equations 2.1 and 2.2 are used to produce the circuit diagram of Figure 1.2(d) which is the equivalent of circuit diagram in
= + (2.2)
Figure 1.2(c).
Figure 1.2(c) Figure 1.2(d) Figure 1.2(c): NOR gates JKFF based on Kmap
Figure 1.2(d): NOT, AND & OR gates JKFF based on characteristic equations

OPTION 1: DESIGNING FLIP FLOP EXTENSION
0 AT 87.5% (REST 1 0)
+1 = + = ( + ) (3.1)
NAND GATES (1, 2, 3)
+ = + = (. )
Figure 2.1(a): Logic Circuit of JKFF Extension 0 at 87.5% (NAND Gate Configuration)
The complete Logic Circuit Diagrams based on the Kmap analysis and the characteristic equations of 3.1 and 3.2 as derived from the state diagram excitation table are constructed in Figures 2.2(b) and 2.2(c) respectively. These two circuit diagrams perform the same memory element functions.
NOR GATES
.
+ = ( + ) =
(
) (. )
+ +
+1 = + (3.2)
NAND GATES (4, 5)
+ = + = . (. )
NOR GATES
Figure 2.2(b) Figure 2.2(c)
Figure 2.2(b): JKFF Extension0 at 87.5% using NAND gates based on K map
Figure 2.2(c): JKFF Extension0 at 87.5% using NOT, AND & OR gates based on characteristic equations
= + (3.2)
Substitute equation (3.2b) into equation (3.2), we have
+1 = + + (3.2)

OPTION 2: DESIGNING FLIP FLOP EXTENSION 1 AT 87.5% (REST 0 1)
+1
= +
= ( + ) (4.1)
+ =
(. )
NAND (1, 2, 3)
+ +
Combining equations (3.1a) & (3.2a) to produce NAND gate configuration of Figure 2.1a; while the combination of equations (3.1b) & (3.2e) to produce NOR gate
+
= + = .
(. )
configuration is not feasible because equation (3.1b) = equation (3.2e).
NOR
+ = ( + ) = + ( +
) (. )
+1 = + (4.2)
NAND (4, 5)
+ = + = (. )

OPTION 3: FLIP FLOP EXTENSION; NO REST
NOR
.
STATES (100%) SUBSTITUTE J = X AND K = Y
+1 = Y + + Y
= + (4.2)
= ( Y + ) + Y (5.1)
Substitute equation (4.2b) into equation (4.2), we have
+1
= + + (4.2)
= + + (. )
NAND GATES (1, 2, 3, 4)
+1 = Y + + Y
+
Combining equations (4.2a) & (4.1a) to produce NAND gate
= Y . . Y
(5.1)
configuration of Figure 3.1a; while the combination of equations (4.1b) & (4.2e) to produce NOR gate configuration is not feasible because equation 4.1b = 4.2e.
+ == . . Y (. )
NORGATES (4, 6, 7, 8)
Replace
= + (5.1)
= X + (5.1)
Figure 3.1(a): Logic Circuit of JKFF Extension 1 at 87.5% (NAND Gate Configuration)
= X + (5.1) Substitute equations (5.1b), (5.1c) & (5.1d) into equation (5.1a), we have
The complete Logic Circuit Diagrams based on the Kmap analysis and the characteristic equations of 4.2 and 4.1 as derived from the state diagram excitation Table are constructed in Figures 3.1(b) and 3.1(c) respectively. These two circuit diagrams perform the same memory element functions.
+ = X + + X + + + (. )
+ = X + + X + + + (. )
+1 = + +
= ( + ) + (5.2)
NAND GATES (5, 6, 7, 8)
+ = + +
= . . X . . (. )
NOR GATES (1, 2, 3, 4)
Replace
= +
(5.2)
= + (5.2)
= + (5.2)
Figure 3.1(b) Figure 3.1(c)
Figure 3.1(b): JKFF Extension1 at 87.5% using gates NAND based on
Substitute equations (5.2b), (5.2c) & (5.2d) into equation (5.2), we have
+ = + + + + + (. )
Kmap
+ + + + +
+ + + + +
Figure 3.1(c): JKFF Extension1 at 87.5% using NOT, AND & OR
+
= (. )
gates based on characteristic equations
Combining equations (5.1a) & (5.2a) will produce NAND gate configuration of Figure 4.1a; while combining
equations (5.1f) &(5.2f) will produce NOR gate configuration of Figure 4.1b
Figure 4.1(a): Logic Circuit of XYFF No Rest at 100% (NAND Gate Configuration)
Figure 4.1(b): Logic Circuit of XYFF No Rest at 100% (NOR Gate Configuration)
The complete Logic Circuit Diagrams based on the Kmap analysis and the characteristic equations of 5.1 and 5.2 as derived from the state diagram excitation Table are constructed in Figures 4.1(c) and 4.1(d) respectively. These two circuit diagrams perform the same memory element functions.
Figure 4.1 (c) Figure 4.1 (d)
Figure 4.1(c): XYFF Extension at 100% using NOR gates based on K map
Figure 4.1(d): XYFF Extension 100% using NOT, AND & OR gates based on characteristic equations

SUMMARY OF THE VARIOUS FLIP FLOPS
DESIGN
Illustrated in Table 1.5 is the summary of the various Flip Flops design with the aim of verifying their gate structures and numbers.

CONCLUSIONS
Previous study revealed that very little research have been carried out on Flip Flops comparative analysis in the 100%, 87.5% and 75% active states utilization on digital device applications. In this paper, a new approach of designing memory element (Flip Flop) with its active states utilization of 87.5% and or 100% as against the conventional Flip Flops at 50% and 75% active states utilization which will enhance memory performance have been developed. This is evidence in section 7 and 8 where the Flip Flop Extensions at 87.5% active states utilization is designed with one gate less than the conventional JKFlip Flop. The uniqueness of this study is that computer memory speed performance can be enhanced through conventional JKFF modification just as it is currently being done with its processor counterpart. This is a great advantage in performance over the conventional Flip Flops because fewer gates enhance performance (i.e., gate delay represents performance). The 87.5% Flip Flop extension memory cell is also portable (less transistors) and cheaper because it requires fewer transistors as against the conventional Flip Flops. An important issue in digital device design is that numbers of transistors represent hardware cost because in essence, maximizing performance and minimising cost in digital devices are part of the factors in seeking alternative design on more efficient and effective Flip flops.
Efforts should be geared towards verifying the effectiveness and efficiency of these newly design Flip Flops Extension over the existing conventional Flip Flops.
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