The problem presents several questions related to computer science concepts. We will focus on question (1b) which asks to convert the decimal number 158 into its octal equivalent and question (2) which deals with logic gates. In question (2), we are given a circuit diagram with NAND gates. We need to determine the output of pin 3 given the inputs of pins 1 and 2, and the output of pin 13 given the inputs of pins 11 and 12.

1. Problem Description

The problem presents several questions related to computer science concepts. We will focus on question (1b) which asks to convert the decimal number 158 into its octal equivalent and question (2) which deals with logic gates. In question (2), we are given a circuit diagram with NAND gates. We need to determine the output of pin 3 given the inputs of pins 1 and 2, and the output of pin 13 given the inputs of pins 11 and

1

2.

2. Solution Steps

(1b) Converting 158 to Octal:

To convert a decimal number to octal, we repeatedly divide the decimal number by 8 and record the remainders. The octal equivalent is obtained by writing the remainders in reverse order.

$158 \div 8 = 19$ with a remainder of $6$

$19 \div 8 = 2$ with a remainder of $3$

$2 \div 8 = 0$ with a remainder of $2$

The remainders in reverse order are 2, 3, and

6.

(2a) Analyzing the Logic Circuit:

The gate connecting pins 1, 2 and 3 is a NAND gate. A NAND gate outputs 0 only if both inputs are

1. Otherwise, it outputs

1. The inputs are pin 1 = 0 and pin 2 =

1. Since not both inputs are 1, the output (pin 3) is

1.

(2b) Analyzing the Logic Circuit:

The gate connecting pins 11, 12 and 13 is a NAND gate.

The inputs are pin 11 = 0 and pin 12 =

1. Since not both inputs are 1, the output (pin 13) is

1.

3. Final Answer

(1b) The octal equivalent of 158 is

2

3

6. (2a) The value of pin 3 is

1. (2b) The value of pin 13 is

1.