Wed Sep 28

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

+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.

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

- \(12\) = 1100
- \(17\) = 10001
- \(41\) = 101001
- \(31\) = 11111

+4 Convert the following 5-bit

**signed two’s complement**binary numbers into base ten.**Hint:**‘signed’ means the results can be negative!- 11100 = \(-4\), because it’s \(-16+8+4\)
- 00111 = \(+7\), because it’s \(4+2+1\)
- 11110 = \(-2\), because it’s \(-16+8+4+2\)
- 11001 = \(-7\), because it’s \(-16+8+1\)

+4 Convert the hexadecimal number

`2D3`

to binary.0010 1101 0011

+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`

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