Question

Boolean algebra simplifcation problem :

How to simply this boolean equation: L = SH' + SH + S'H'

Answer 1

The logical expression shows the logical gates (AND, OR and NOT gate) used and by simplifying the logical expression we can identify the minimum no of logical gates required to get the same output as the previous one.

The given logical expression is:

L = SH’ + SH + S’H’

The output table for this expression will be:

S	H	SH’	SH	S’H’	L = SH’ + SH + S’H’
0	0	0*1=0	0*0=0	1*1=1	0+0+1=1
0	1	0*0=0	0*1=0	1*0=0	0+0+0=0
1	0	1*1=1	1*0=0	0*1=0	1+0+0=1
1	1	1*0=0	1*1=1	0*0=0	0+1+0=1

Now solving the equation.

L = SH’ + SH + S’H’

L = S (H + H’) + S’H’     à taking S common

Now since H + H’ =1 and S*1 = S, so the equation will be:

L = S + S’H’

Now, since A + A’B = A + B (basic rule), hence the output will be:

L = S + H’

The output table for this expression will be:

S	H	H’	L = S + H’
0	0	1	0+1=1
0	1	0	0+0=0
1	0	1	1+1=1
1	1	0	1+0=1

Which same as the above one.