Problem Set Answers: Binary and Hexadecimal

1. Convert the following decimal numbers to binary:
1. 75₁₀ = 100 1011₂
2. 233₁₀ = 1110 1001₂
3. 1191₁₀ = 100 1010 0111₂
4. 807₁₀ = 11 0010 0111₂
5. 14,188₁₀ = 11 0111 0110 1100₂
2. Convert the following binary numbers to decimal:
1. 10 1101₂ = 45₁₀
2. 110 0101 0001₂ = 1617₁₀
3. 11 1110₂ = 62₁₀
4. 1000 1110₂ = 142₁₀
5. 11 0100 1111₂ = 847₁₀
3. Convert the following binary numbers to hexadecimal:
1. 101 1101 1011₂ = 5DB₁₆
2. 1 1101 1011 0100₂ = 1DB4₁₆
3. 1 0011 0110₂ = 136₁₆
4. 1000 1111 0111 1100₂ = 8F7C₁₆
5. 110 0101 1001 1011₂ = 659B₁₆
4. Convert the following hexadecimal numbers to binary:
1. 241₁₆ = 10 0100 0001₂
2. EA₁₆ = 1110 1010₂
3. 5B7₁₆ = 101 1011 0111₂
4. 3F06₁₆ = 11 1111 0000 0110₂
5. 80C9₁₆ = 1000 0000 1100 1001₂
5. Perform the following additions and subtractions. Assume that all numbers are in sign and magnitude base 2 representation.
   1. 11101 + 110101 = 101 0010
   2. 110011 + 1111010 = 1010 1101
   3. 100110 + 11010 = 100 0000
   4. 1010111 + 10011 = 110 1010
   5. 1011010110 + 11100111 = 11 1011 1101
6. Perform the following additions and subtractions. Assume that all numbers are in hexadecimal.
   1. AD85 + 6F = ADF4
   2. 8726 + 9583 = 11CA9
   3. E3B4 + 27D1 = 10B85
   4. 96F + 3A8C = 43FB
   5. 246 + ACE = D14

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