cs101 assignmnt solution

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CS101

ASSIGNMENT NO 1

Q no 1 solution:

Convert the decimal no into binary and then again into binary:

i)4789

Conversion into binary:

Deviser	Dividend	Reminder
2	4789	1
2	2394	0
2	1197	1
2	598	0
2	299	1
2	149	1
2	74	0
2	37	1
2	18	0
2	9	1
2	4	0
2	2	0
2	0	1

 

4789=(1001010110101)₂

Binary to decimal no:

(1001010110101)₂=1.2¹²+0.2¹¹+0.2¹⁰+1.2⁹+0.2⁸+1.2⁷+0.2⁶+1.2⁵+1.2⁴+0.2³+1.2²+0.2¹+1.2⁰

 (1001010110101)₂=4096+0+0+512+128+0+32+16+0+4+0+1

(1001010110101)₂=4789

ii)8735

Deviser	Dividend	Reminder
2	8735	1
2	4367	1
2	2183	1
2	1091	1
2	545	1
2	272	0
2	136	0
2	68	0
2	34	0
2	17	1
2	8	0
2	4	0
2	2	0
2	0	1

 

_8735=(10001000011111)₂

Binary to decimal:

(10001000011111)₂=1.2¹⁴+0.2¹³+0.2¹²+0.2¹¹+1.2¹⁰+0.2⁹+0.2⁸+0.2⁷+0.2⁶+1.2⁵+1.2⁴+1.2³+1.2²+1.2¹+1.2⁰

(10001000011111)₂=_(8192+0+0+0+512+0+0+0+0+16+8+4+2+1)

(10001000011111)₂=_8735

Q NO2 SOLUTION:

Solve Boolean expression:

[(A⊕D).(A+B)].[( B ̅+C ̅) ⊕(B+C+D)]

A	B	C	D
0	0	0	0	0	0	1	0	1	0	0
0	0	0	1	1	0	1	1	0	0	0
0	0	1	0	0	0	1	1	0	0	0
0	0	1	1	1	0	1	1	0	0	0
0	1	0	0	0	1	1	1	0	0	0
0	1	0	1	1	1	1	1	0	1	0
0	1	1	0	0	1	0	1	1	0	0
0	1	1	1	1	1	0	1	1	1	1
1	0	0	0	1	1	1	0	1	1	1
1	0	0	1	0	1	1	1	0	0	0
1	0	1	0	0	1	1	1	0	0	0
1	0	1	1	0	1	1	1	0	0	0
1	1	0	0	1	1	1	0	1	1	1
1	1	0	1	0	1	1	1	0	0	0
1	1	1	0	1	1	0	1	1	1	1
1	1	1	1	0	1	0	1	1	0	0