Positive logic nand gate equivalent negative logic nor gate

(b) (27.5) 10 to binary ( )2, then to octal ( )8

(ii) Convert the following expression into sum-of-products and product-of-sums forms: (A+ CD) (BD+AČ)

Whole number part:

365 ÷ 2 = 182 remainder 1

11 ÷ 2 = 5 remainder 1

5 ÷ 2 = 2 remainder 1

0.7 × 2 = 1.4 (integer part: 1)

0.4 × 2 = 0.8 (integer part: 0)

0.8 × 2 = 1.6 (integer part: 1)

The fractional part in binary is 101100.

1011 = B

0110 = 6

The whole number part can be converted directly, while the fractional part can be converted by multiplying it by 2 repeatedly and taking the integer part at each step.

Whole number part:

1 ÷ 2 = 0 remainder 1

The whole number part in binary is 11011.

To convert to octal, we group the binary digits into groups of three, starting from the left of the decimal point:

011 011.100

The octal representation of (27.5)10 is 33.4.

(ii) The given expression is (A + CD) (BD + AČ). To convert it into sum-of-products form, we expand and distribute the terms:

= (A + CD + BD + AČ)(A + CD + BD +AČ) Č

(iii) A positive logic NAND gate is a negative logic NOR gate and vice versa.

(iv) Designing a 3-to-8-line decoder using two 2-to-4-line decoders and 8 2-input AND gates:

A 3-to-8-line decoder takes three input lines (A, B, and C) and produces eight output lines (Y0 to Y7) based on the input combination.

4. Connect the outputs (Y0 to Y3) of the first 2-to-4-line decoder to the first AND gate inputs.

5. Connect the outputs (Y0 to Y3) of the second 2-to-4-line decoder to the second AND gate inputs.