# CS2100 Assignment 2

Name : Ethan Chen Ee Shuen
Tutorial Group : T11

2a)
Jump

2b)

1) 0010
2) 0001 0000 0001 0000 0000 0000 0000
3) 0010 0001 0000 0001 0000 0000 0000

3a) (View Next page if this page doesn't load)

A·B' + A'·C + B·C'·D
A	B	C	D	X
0	0	0	0	0
0	0	0	1	0
0	0	1	0	1
0	0	1	1	1
0	1	0	0	0
0	1	0	1	1
0	1	1	0	1
0	1	1	1	1
1	0	0	0	1
1	0	0	1	1
1	0	1	0	1
1	0	1	1	1
1	1	0	0	0
1	1	0	1	1
1	1	1	0	0
1	1	1	1	0

a	b	c	d	X
0	0	0	0	0
0	0	0	1	0
0	0	1	0	1
0	0	1	1	1
0	1	0	0	0
0	1	0	1	1
0	1	1	0	1
0	1	1	1	1
1	0	0	0	1
1	0	0	1	1
1	0	1	0	1
1	0	1	1	1
1	1	0	0	0
1	1	0	1	1
1	1	1	0	0
1	1	1	1	0
F(A,B,C,D)
= A·B' + A'·C + B·C'·D

Let the negation of F to be G

Then,
G(A, B, C, D)
= (A·B' + A'·C + B·C'·D)' 
= (A' + B)·(A + C')·(B' + C + D') //De Morgan's Theorem and Involution
= ((A' + B)·A +(A' + B)·C')·(B' + C + D') //Distribution Law
= ((A'·A + B·A) +(A'·C' + B·C'))·(B' + C + D') //Distribution Law 
= ((0 + B·A) + (A'·C' + B·C'))·(B' + C + D') //Inverse Law 
= (B·A +A'·C' + B·C')·(B' + C + D') //Identity & Distribution Law
= (B·A +A'·C' + B·C')· B' + (B·A +A'·C' + B·C')·C + (B·A +A'·C' + B·C')·D' //Distribution Law 
= (B·A·B' + A'·C'·B' + B·C'·B') + (B·A·C + A'·C'·C + B·C'·C) + (B·A·D' + A'·C'·D' + B·C'·D') //Distribution Law 
= (0 + A'·C'·B' + 0) + (B·A·C + 0 + 0) + (B·A·D' + A'·C'·D' + B·C'·D') //Inverse Law
= A'·C'·B' + B·A·C + B·A·D' + A'·C'·D' + B·C'·D' //Identity Law

F(A,B,C,D)
= (A'·C'·B' + B·A·C + B·A·D' + A'·C'·D' + B·C'·D')' 
= (A'·C'·B')'·(B·A·C)'·(B·A·D')'·(A'·C'·D')'·(B·C'·D')' //De Morgan's Theorem
= (A+C+B)·(B'+A'+C')·(B'+A'+D)·(A+C+D)·(B'+C+D) //De Morgan's Theorem and Involution
= (A+C+B)·(B'+C+D)·(B'+A'+C')·(B'+A'+D)·(A+C+D) //Commutative
= (A+C+B)·(B'+C+D)·(A+C+D)·(B'+A'+C')·(B'+A'+D) //Commutative
= (A+C+B)·(B'+C+D)·(B'+A'+C')·(B'+A'+D) //Consensus
= (A+C+B).(B'+(A'+C').(C+D).(A'+D)) //Distribution law
= (A+C+B).(B'+(A'+C').(C+D)) //Consensus
= (A+C+B).(B'+A'+C').(B'+C+D) //Distribution law