Question

Evaluate each of these expressions.

$$\begin{gathered} \mathbf{a}\mathbf{)}\mathbf{}\mathbf{11000}\mathbf{\wedge }\mathbf{(}\mathbf{01011}\mathbf{\vee }\mathbf{11011}\mathbf{\left)} \\ \mathbf{b}\mathbf{\right)}\mathbf{}\mathbf{(}\mathbf{01111}\mathbf{\wedge }\mathbf{10101}\mathbf{)}\mathbf{\vee }\mathbf{01000} \\ \mathbf{c}\mathbf{)}\mathbf{}\mathbf{(}\mathbf{01010}\mathbf{\oplus }\mathbf{11011}\mathbf{)}\mathbf{\oplus }\mathbf{01000} \\ \mathbf{d}\mathbf{)}\mathbf{}\mathbf{(}\mathbf{11011}\mathbf{\vee }\mathbf{01010}\mathbf{)}\mathbf{\wedge }\mathbf{(}\mathbf{10001}\mathbf{\vee }\mathbf{11011}\mathbf{)} \end{gathered}$$

Short answer

a) 11000

b) 01101

c) 11001

d) 11011

Step-by-step solution

Definition of bitwise function

A bitwise function is the one which operates on bit patterns at the individual level.

Expression in a)

We write given expression as,

$$\begin{gathered} 11000\wedge (01011\vee 11011) \\ =11000\wedge 11011 \\ =11000 \end{gathered}$$

Expression in b)

We write given expression as,

$$\begin{gathered} (01111\wedge 10101)\vee 01000 \\ =00101\wedge 01000 \\ =01101 \end{gathered}$$

Expression in c)

We write given expression as,

$$\begin{gathered} (01010\oplus 11011)\oplus 01000 \\ =00101\oplus 01000 \\ =11001 \end{gathered}$$

Expression in d)

We write given expression as,

$$\begin{gathered} (11011\vee 11011)\wedge (10001\vee 11011) \\ =11011\wedge 11011 \\ =11011 \end{gathered}$$