Question 1

Convert the decimal number 25 to binary.

Accepted Answer

25 ÷ 2 = 12 remainder 1, 12 ÷ 2 = 6 remainder 0, 6 ÷ 2 = 3 remainder 0, 3 ÷ 2 = 1 remainder 1, 1 ÷ 2 = 0 remainder 1, reading remainders bottom-to-top gives 11001.

Question 2

What is the hexadecimal equivalent of the binary number 10101010?

Accepted Answer

Binary 10101010 groups into 1010 (10 in decimal = A in hex) and 1010 (10 in decimal = A in hex), giving AA.

Question 3

Convert the octal number 75 to decimal.

Accepted Answer

75 in octal = (7 × 8¹) + (5 × 8⁰) = 56 + 5 = 61 in decimal; rechecking: 7×8 + 5 = 61 is correct, but the answer key shows 63—verify: actually 7×8+5=61 (answer B is correct).

Question 4

How many bits are required to represent the decimal number 100 in binary?

Accepted Answer

100 in binary is 1100100, which requires 7 bits; the highest power of 2 less than 100 is 2⁶ = 64, so 7 bits are needed.

Question 5

What is the decimal value of the hexadecimal number 2F?

Accepted Answer

2F in hexadecimal = (2 × 16¹) + (15 × 16⁰) = 32 + 15 = 47 in decimal.

Question 6

Convert the binary number 11110000 to its octal equivalent.

Accepted Answer

Binary 11110000 groups into 011 (3 in octal), 110 (6 in octal), 000 (0 in octal), giving 360 in octal.

Question 7

Convert the binary number 10101010 to hexadecimal.

Accepted Answer

Split into two 4-bit groups: 1010 = A and 1010 = A, giving AA in hexadecimal.

Question 8

Convert the hexadecimal number 2A to decimal.

Accepted Answer

(2 × 16¹) + (A × 16⁰) = 32 + 10 = 42 in decimal.

Question 9

Convert the decimal number 45 to binary.

Accepted Answer

45 ÷ 2 = 22 R 1, 22 ÷ 2 = 11 R 0, 11 ÷ 2 = 5 R 1, 5 ÷ 2 = 2 R 1, 2 ÷ 2 = 1 R 0, 1 ÷ 2 = 0 R 1, reading remainders upward gives 101101.

Question 10

What is the hexadecimal equivalent of the binary number 11010110?

Accepted Answer

Split binary into two groups of 4 bits: 1101 = D (13) and 0110 = 6, so the hexadecimal is D6.

Question 11

Convert the octal number 157 to decimal.

Accepted Answer

(1 × 8²) + (5 × 8¹) + (7 × 8⁰) = 64 + 40 + 7 = 111 decimal, but correct answer is 119; recalculating: (1×64) + (5×8) + (7×1) = 64 + 40 + 7 = 111—verification shows option B (119) requires 163 octal, so A is correct as 111.

Question 12

Which hexadecimal number equals the decimal value 255?

Accepted Answer

255 = (15 × 16) + 15 = F × 16 + F = FF in hexadecimal.

Question 13

What is the binary representation of the octal digit 5?

Accepted Answer

The octal digit 5 directly converts to 101 in binary (4 + 1).

Question 14

Convert the hexadecimal number 2F4 to its decimal equivalent.

Accepted Answer

2F4₁₆ = (2 × 16²) + (15 × 16¹) + (4 × 16⁰) = 512 + 240 + 4 = 756₁₀

Question 15

A system stores a number in octal as 365. What is the binary representation of this octal number?

Accepted Answer

365₈ converts to binary by converting each octal digit: 3=011, 6=110, 5=101, resulting in 011110101₂

CAPF AC Number Systems (Binary Decimal Hex Octal)

Number Systems (Binary Decimal Hex Octal) — Practice Questions