Mon Feb 2

You have up to 25 minutes. You may use a standard calculator, but no text book or notes.

Suppose we have the digits

**152**, written using base**six.**What quantity does that represent, expressed in base**ten?**+2The column values in base six are (left to right) 36, 6, and 1. So this number is 1×36 + 5×6 + 2×1 = 36 + 30 + 2 = 68.

Convert the following

**unsigned**binary numbers into base ten. +4- 11100 = 28
- 11011 = 27
- 11001 = 25
- 111 = 7

Convert the following base ten numbers into binary using

**5-bit signed two’s complement**+4- \(-12\) = 10100
- \(13\) = 01101
- \(-8\) = 11000
- \(-1\) = 11111

Add and verify the following

**unsigned**(**not**fixed-size) binary numbers. +4We

*keep the extra carry bit,*because these are not fixed width!`1 1 1 1 1 1 1 1 0 0 = 12 1 1 1 1 1 = 31 + 1 0 0 1 1 0 = 38 + 1 0 0 1 0 0 = 36 —————————————— —————————————— 1 1 0 0 1 0 = 50 1 0 0 0 0 1 1 = 67`

Convert the hexadecimal number

`27C`

to binary. +30010 0111 1100

Convert the octal number

`615`

to binary. +3110 001 101