Question 9: Find the binary, hexadecimal, or octal number that is equivalent to the decimal value 161. Question 10: Find the number with the least value among a binary, a decimal, a hexadecimal, and an octal number.

Here are the solutions to questions 9 and

1

0.

1. Problem Description

Question 9: Find the binary, hexadecimal, or octal number that is equivalent to the decimal value

1

6

1. Question 10: Find the number with the least value among a binary, a decimal, a hexadecimal, and an octal number.

2. Solution Steps

Question 9:

Convert each option to decimal to check for equivalence.

1) $11111000_2 = 1 \cdot 2^7 + 1 \cdot 2^6 + 1 \cdot 2^5 + 1 \cdot 2^4 + 1 \cdot 2^3 + 0 \cdot 2^2 + 0 \cdot 2^1 + 0 \cdot 2^0 = 128 + 64 + 32 + 16 + 8 = 248$

2) $10100001_2 = 1 \cdot 2^7 + 0 \cdot 2^6 + 1 \cdot 2^5 + 0 \cdot 2^4 + 0 \cdot 2^3 + 0 \cdot 2^2 + 0 \cdot 2^1 + 1 \cdot 2^0 = 128 + 32 + 1 = 161$

3) $A2_{16} = 10 \cdot 16^1 + 2 \cdot 16^0 = 160 + 2 = 162$

4) $510_8 = 5 \cdot 8^2 + 1 \cdot 8^1 + 0 \cdot 8^0 = 5 \cdot 64 + 8 + 0 = 320 + 8 = 328$

Question 10:

Convert each option to decimal to compare their values.

1) $1100011_2 = 1 \cdot 2^6 + 1 \cdot 2^5 + 0 \cdot 2^4 + 0 \cdot 2^3 + 0 \cdot 2^2 + 1 \cdot 2^1 + 1 \cdot 2^0 = 64 + 32 + 2 + 1 = 99$

2) $120_{10} = 120$

3) $FE_{16} = 15 \cdot 16^1 + 14 \cdot 16^0 = 240 + 14 = 254$

4) $67_8 = 6 \cdot 8^1 + 7 \cdot 8^0 = 48 + 7 = 55$

The least value is

5

5.

3. Final Answer

Question 9: 2) 101000012

Question 10: 4) 678