An Approach for Implementing State Machines with Online Testability

Table 1

Example FSM transition table and resulting output equations.

Present state				Inputs		Next state				Outputs
$R_3$	$R_2$	$R_1$	R 0	$X_1$	$X_0$	$Q_3$	$Q_2$	$Q_1$	$Q_0$	$F_1$	F 0
1	1	0	0	0	0	1	1	0	0	0	1
				0	1	1	0	1	0	0	0
				1	0	0	0	1	1	0	1
				1	1	0	1	0	1	1	1
1	0	1	0	0	0	0	1	1	0	1	1
				0	1	0	1	0	1	1	0
				1	0	0	0	1	1	1	1
				1	1	1	0	0	1	0	0
1	0	0	1	0	0	1	1	0	0	0	1
				0	1	1	1	0	0	0	0
				1	0	1	0	0	1	1	0
				1	1	1	0	0	1	1	0
0	1	1	0	0	0	0	1	0	1	0	1
				0	1	0	1	1	0	1	1
				1	0	0	1	1	0	1	1
				1	1	1	1	0	0	1	0
0	1	0	1	0	0	1	0	0	1	1	0
				0	1	0	0	1	1	0	0
				1	0	0	1	0	1	1	1
				1	1	1	0	0	1	1	1
0	0	1	1	0	0	1	1	0	0	1	0
				0	1	1	0	1	0	0	1
				1	0	0	1	1	0	0	1
				1	1	0	1	0	1	0	0
$F_0=\mathrm{\hspace{0.17em}\hspace{0.17em}}{R}_3{R}_2\mathrm{\hspace{0.17em}\hspace{0.17em}}(X_1+{\bar{X}}_1{\bar{X}}_0)+R_3{R}_1\mathrm{\hspace{0.17em}\hspace{0.17em}}({\bar{X}}_0)+R_3{R}_o\mathrm{\hspace{0.17em}\hspace{0.17em}}({\bar{X}}_1{\bar{X}}_0)+R_2{R}_1\mathrm{\hspace{0.17em}\hspace{0.17em}}({\bar{X}}_1+X_1{\bar{X}}_0)+R_2{R}_0\mathrm{\hspace{0.17em}\hspace{0.17em}}(X_1)+R_1{R}_0\mathrm{\hspace{0.17em}\hspace{0.17em}}(X_1{\bar{X}}_0+{\bar{X}}_1{X}_0)$
$F_1=\mathrm{\hspace{0.17em}\hspace{0.17em}}{R}_3{R}_2\mathrm{\hspace{0.17em}\hspace{0.17em}}(X_1{X}_0)+R_3{R}_1({\bar{X}}_1\mathrm{\hspace{0.17em}\hspace{0.17em}}+\mathrm{\hspace{0.17em}\hspace{0.17em}}{X}_1{\bar{X}}_0)+R_3{R}_0(X_1)+R_2{R}_1(X_1+{\bar{X}}_1{X}_0)+\mathrm{\hspace{0.17em}\hspace{0.17em}}{R}_2{R}_0\mathrm{\hspace{0.17em}\hspace{0.17em}}(X_1+{\bar{X}}_1{\bar{X}}_0)\mathrm{\hspace{0.17em}\hspace{0.17em}}+\mathrm{\hspace{0.17em}\hspace{0.17em}}{R}_1{R}_0({\bar{X}}_1{\bar{X}}_0)$