### Digital Electronics Objectives Part 08

141 . A NAND gate is called a universal logic element because any logic function can be realized by NAND gates alone.

142 . The Boolean expression A𝐵𝐶 + AB̅̅̅̅C̅+A̅BC̅ + A̅B̅C is equal to 𝐁̅ 𝐂̅+𝐀̅𝐂̅+𝑨𝐁̅.

143 . The Boolean expression ABC+A̅BC+AB̅C+ABC̅+A̅B̅C̅ + A̅B̅C̅ will be equal to 𝐂̅+𝐁̅+𝐀

144 . The Boolean expression A(A+B+C)(A̅+B+C)(A+B̅+C)(A+B̅+C̅) will be same as 𝐀(𝐁̅+𝐂).

145 . The Boolean expression (A+B+C)(A+B̅+C̅)(A+B̅+C̅)(A̅+B̅+C) can be simplified as A.

146 . The expression XY (𝑋YZ + 𝑋𝑌𝑍 + 𝑋𝑌𝑍 ) when simplified will become 0.

147 . The expression XY + XYZ + XY𝑍 + 𝑋YZ when simplified will become Y.

148 . The expression ABC(AB𝐶 + AB̅C+A̅BC) when simplified for no assignment of binary values will take the value 1.

149 . The expression AB + A𝐵 + A𝐶 + 𝐴𝐶 will be equal to 1.

150 . The expression of (A + BC + AB) will be 𝐀̅(𝐁̅+𝐂̅).

151 . The complement of (A+B)(B+C)(A+C) will be 𝐀̅
𝐁̅+𝐁̅𝐂̅+𝐀̅𝐂̅.

152 . The following expression when converted to sum of products from, will become (𝑨BC + A𝑩C + AC + BC).

153 . The expression ((A̅+C)(A̅+B̅+C̅)(A+B̅) when converted to sum of product form will become 𝐀𝐁̅+𝐀𝐂̅+𝐀𝐁𝐂+𝐀𝐁𝐂̅+𝐀̅ 𝐁𝐂+𝐁𝐂̅.

154 . The expression (A+C)(A𝐵 + AC)(𝐴𝐶 + 𝐵) when converted to sum of products from will become AB + ABC.(𝐗̅

155 . 𝐘̅𝐙̅+𝐗𝐘̅𝐙) is the Boolean expression (in sum of products form) for a logic circuit when will have all output when X = 0, Y = 0 and Z = 1 and a O output for all other input state.

156 . for the logic diagram shown in Fig. 25 the output will be 𝑿𝒀 𝒁+𝑿𝒀𝒁.

157 . XY + X𝑍 is the Boolean expression in the sum of products from for a logical network which will have a 1 output when
X = 0, Y = 1 , Z = 1
X = 1, Y = 1, Z =
X = 1, Y = 0, Z =
X = 1, Y = 1 , Z = 1

158 .
Inputs X Y Z Output F1 Output F2 Output F3 000 0 1 001 0 1 1 010 1 1 1 011 1 0 0 100 0 0 0

159 . The sum of the products expression for the above table will be Y𝒁 + 𝒀Z.

160 . The product of the sum form of expression for the above truth table will be (X +Y) (𝒀 + 𝒁).