# 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``

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``````