Solutions to binary practice problems

1. Convert the following base ten (decimal) numbers into binary.

   1. 6    = 110₂
   2. 18    = 10010₂
   3. 51    = 110011₂
   4. 63    = 111111₂

2. Convert the following unsigned binary numbers into base ten.

   1. 1010    = 10₁₀ (ten)
   2. 1101    = 13₁₀
   3. 1000    = 8₁₀
   4. 10001    = 17₁₀

3. What do all odd numbers have in common, when written in binary? (Hint: try writing the quantities 3, 5, 7, 9, 11 in binary.)

   Odd numbers always end with a 1.

4. Using 7-bit signed (two’s complement) binary numbers, what is the largest positive number? What is the most negative number?

   Largest is +63, most negative is –64.

5. Convert the following 5-bit signed (two’s complement) binary numbers into base ten.

   1. 01101    = +13
   2. 01111    = +15
   3. 10011    = –13
   4. 11111    = –1

6. Convert the following 16-bit binary number into hexadecimal, and then into octal.

   0 1 1 1 1 1 1 1 0 0 1 1 1 0 1 0

   Hexadecimal: 0111,1111,0011,1010 = 7F3A
   Octal: 0,111,111,100,111,010 = 77472 (I initially had a mistake here.)

7. Convert the following hexadecimal numbers into binary:

   1. 9D    = 1001,1101
   2. C4    = 1100,0100
   3. A17E    = 1010,0001,0111,1110

8. Add and verify the following unsigned binary numbers.

   We keep the extra carry bit, because these are unsigned and I didn’t say they were fixed width!

   1 1 1 1 1 1                      1     1
     1 0 1 1 1 1  = 47                1 1 0 1 1 1  = 55
   +   1 1 1 0 1  = 29              + 1 0 0 1 0 0  = 36
   ——————————————                   ——————————————
   1 0 0 1 1 0 0  = 76              1 0 1 1 0 1 1  = 91