# Quiz 2 Solutions

Wed Sep 28

You have up to 20 minutes. You may use a standard calculator if necessary, but no text book or notes.

1. +4 Suppose we have the digits 154, written using base six. What quantity does that represent, expressed in base ten?

The column values in base six are (left to right) 36, 6, and 1. So this number is 1×36 + 5×6 + 4×1 = 36 + 30 + 4 = 70.

2. +4 Convert the following base ten numbers into binary. Use as many bits as you need.

1. $$12$$    = 1100
2. $$17$$    = 10001
3. $$41$$    = 101001
4. $$31$$    = 11111
3. +4 Convert the following 5-bit signed two’s complement binary numbers into base ten. Hint: ‘signed’ means the results can be negative!

1. 11100    = $$-4$$, because it’s $$-16+8+4$$
2. 00111    = $$+7$$, because it’s $$4+2+1$$
3. 11110    = $$-2$$, because it’s $$-16+8+4+2$$
4. 11001    = $$-7$$, because it’s $$-16+8+1$$

1. +4 Convert the hexadecimal number 2D3 to binary.

0010 1101 0011

2. +4 Convert this binary number to octal: 1 1 1 0 0 1 1 1 0 1

Group it from right to left and add leading zeroes as necessary: (001) (110) (011) (101) and then each group of three bits becomes one octal digit: 1635.