Chapter B, Problem 11E

Explanation of Solution

x2	x1	x0	Only one 0 f1	Even 0’s f2	Unsigned binary x<4 f3	Signed negative number f4
0	0	0	0	0	1	0
0	0	1	0	1	1	0
0	1	0	0	1	1	0
0	1	1	1	0	1	0
1	0	0	0	1	0	1
1	0	1	1	0	0	1
1	1	0	1	0	0	1
1	1	1	0	1	0	1

In the above table, A0, A1, A2 and A3 represent four different inputs and f1, f2, f3 and f4 represents odd parity, even number of 0’s, unsigned binary number less than 4 and signed negative number respectively.

The above K-map diagram describes about the odd parity function. No two bits are mapped and the function is written in sum of products form.

The K-map function is as follows

$f_{\text{1}}{\text{(x}}_0\text{,}{\text{x}}_{\text{1}}\text{,}{\text{x}}_2\text{)}\text{=}\overline{{\text{x}}_{\text{0}}}{\text{x}}_{\text{1}}{\text{x}}_{\text{2}}\text{+}{\text{x}}_{\text{0}}\overline{{\text{x}}_{\text{1}}}{\text{x}}_{\text{2}}\text{+}{\text{x}}_{\text{0}}{\text{x}}_{\text{1}}\overline{{\text{x}}_{\text{2}}}$

The above K-map diagram describes about the even number of 0s function. No two bits are mapped and the function is written in sum of products form.

The K-map function is as follows

$f_2{\text{(x}}_0\text{,}{\text{x}}_{\text{1}}\text{,}{\text{x}}_2\text{)}\text{=}{\text{x}}_{\text{0}}\overline{{\text{x}}_{\text{1}}}\overline{{\text{x}}_{\text{2}}}\text{+}\overline{{\text{x}}_{\text{0}}}{\text{x}}_{\text{1}}\overline{{\text{x}}_{\text{2}}}\text{+}\overline{{\text{x}}_{\text{0}}}\overline{{\text{x}}_{\text{1}}}{\text{x}}_2+{\text{x}}_0{\text{x}}_{\text{1}}{\text{x}}_2$