Computer Number System

Question 1: Binary to Decimal

Convert the binary number 1101 to its decimal equivalent.

• 11

• 12

• 13

• 14

Answer explanation

To convert the binary number 1101 to decimal, we use the formula: (1 * 2^3) + (1 * 2^2) + (0 * 2^1) + (1 * 2^0) = 13. Therefore, the correct answer is 13.

Question 2: Decimal to Binary

Convert the decimal number 25 to its binary equivalent.

• 11001

• 10110

• 10011

• 11100

Answer explanation

To convert decimal 25 to binary, repeatedly divide by 2 and note remainders. Reading remainders from bottom to top gives 11001, which is the binary equivalent.

Question 2: Decimal to Binary

Convert the decimal number 25 to its binary equivalent.

• 11001

• 10110

• 10011

• 11100

Answer explanation

To convert decimal 25 to binary, repeatedly divide by 2 and note remainders. Reading remainders from bottom to top gives 11001, which is the binary equivalent of 25.

Question 3: Decimal to Octal

Convert the decimal number 56 to its octal equivalent.

• 70

• 71

• 72

• 73

Answer explanation

To convert decimal 56 to octal, divide 56 by 8. The remainder of each division gives the octal equivalent. 56 ÷ 8 = 7 with a remainder of 0. Therefore, the octal equivalent is 70.

Question 4: Octal to Decimal

Convert the octal number 34 to its decimal equivalent.

• 28

• 29

• 30

• 31

Answer explanation

To convert octal 34 to decimal, we use the formula: (3 * 8^1) + (4 * 8^0) = 24 + 4 = 28. Therefore, the decimal equivalent of octal 34 is 28.

Question 5: Decimal to Hexadecimal

Convert the decimal number 255 to its hexadecimal equivalent.

• DD

• EE

• FF

• CC

Answer explanation

To convert decimal 255 to hexadecimal, divide by 16: 255 ÷ 16 = 15 remainder 15 (F). The remainder 15 is represented as 'F' in hexadecimal. Therefore, 255 in decimal is 'FF' in hexadecimal.

Question 6: Hexadecimal to Decimal

Convert the hexadecimal number 1A3 to its decimal equivalent.

• 422

• 420

• 421

• 419

Answer explanation

To convert hexadecimal 1A3 to decimal, we multiply each digit by 16 raised to the power of its position. (1*16^2) + (10*16^1) + (3*16^0) = 419.

Question 7: Binary to Hexadecimal

Convert the binary number 10101100 to its hexadecimal equivalent.

• • AB

• • AC

• • AE

• • AD

Answer explanation

To convert binary to hexadecimal, group the binary number into sets of 4 starting from the right. 1010 is A, and 1100 is C. Therefore, 10101100 in binary is equivalent to AC in hexadecimal.

Question 8: Hexadecimal to Binary

Convert the hexadecimal number 3F to its binary equivalent.

• • 111110

• • 111100

• • 111000

• • 111111

Answer explanation

To convert hexadecimal 3F to binary, each hexadecimal digit corresponds to 4 binary digits. 3 in binary is 0011, and F in binary is 1111. Therefore, 3F in binary is 00111111, which is 111111 in short form.

Question 9: Octal to Binary

Convert the octal number 75 to its binary equivalent.

• • 111100

• • 110111

• • 111101

• • 111011

Answer explanation

To convert octal 75 to binary, first convert each octal digit to 3-bit binary. 7 in octal is 111 and 5 is 101. Combine them to get 111101 in binary.