330 DIGITAL BUILDING BLOCKS AND COMPUTER SYSTEMS(b)Y=A·B+B ̄·C+A·C·D+A·B·D
(c)Y=(A ̄+B+C)·(A ̄+B+C)·C ̄
(d)Y=B·C+B ̄·C ̄+A·B ̄·C
6.1.23The truth table forF(A,B,C)=∑
mi( 2 , 3 , 4 ,
5 )is as follows:ABCF0000
0010
0101
0111
1001
1011
1100
1110(a) ExpressFin a canonical sum-of-products
form.
(b) MinimizeFin an SOP form, and obtain a
possible realization.*6.1.24The truth table forF(A,B,C)=
∏
Mi( 0 , 1 , 6 ,
7 )is as follows:ABCF0000
0010
0101
0111
1001
1011
1100
1110(a) ExpressFin a canonical product-of-sums
form.
(b) MinimizeFin a POS form and obtain a pos-
sible realization.
6.1.25Using K maps, simplify the following Boolean
expressions:
(a)F=A·B ̄+A·B
(b)F=A·C+C·D+B·C·D
(c)F=A·B·C ̄+B·C+A·B·D+B·C·D
6.1.26Simplify the following Boolean functions into
their minimum SOP form, by using K maps.
(a)F(A,B)=
∑
mi( 0 , 1 , 3 )(b)F(A,B,C)=∑
mi( 0 , 2 , 3 , 4 , 5 , 6 )
(c)F(A,B,C,D) =∑
mi( 0 , 4 , 5 , 6 , 7 ,
12 , 14 )
(d)F(A,B)=
∏
Mi( 0 , 2 )
(e)F(A,B,C)=
∏
Mi( 0 , 6 )
(f) F(A,B,C,D)=∏
Mi( 1 , 3 , 11 , 14 , 15 )
6.1.27Given the following truth table, design the logic
circuit with the use of a K map by using only two-
input gates.ABCDy00001
00011
00101
00110
01000
01011
01100
01110
10001
10011
10100
10111
11000
11011
11100
111116.1.28For the logic circuit of Figure P6.1.28, construct a
truth table and obtain the minimum SOP expres-
sion.
*6.1.29Simplify the logic circuit of Figure P6.1.29 by
reducing the number of gates to a minimum.
6.1.30Given the following truth table:
(a) Realize the functionfby a K map using 0s.
(b) Realize the functionfby a K map using 1s.xyzf0000
0011
0101
0111
1001
1011
1100
11106.1.31Realize the logic function defined by the following
truth table as the simplest POS form.