###### 1

Use the “Decoder Ring” in Figure 3.6.2 to perform the following arithmetic. Indicate whether the result is “right” or “wrong”.

Unsigned integers: \(\hex{1 + 3}\)

Unsigned integers: \(\hex{3 + 4}\)

Unsigned integers: \(\hex{5 + 6}\)

Signed integers: \(\hex{(+1) + (+3)}\)

Signed integers: \(\hex{(-3) - (+3)}\)

Signed integers: \(\hex{(+3) - (+4)}\)

For unsigned arithmetic, use the two inner rings and pay attention to passing over the top (`C`

). For signed arithmetic, use the outer and inner rings and pay attention to passing over the bottom (`V`

).

Start at the tic mark for \(1\text{,}\) move \(3\) tic marks CW, giving \(4 = \binary{100}_{2}\text{.}\) We did not pass the tic mark at the top, so

`C`

= \(\binary{0}\text{,}\) and the result is correct.Start at the tic mark for \(3\text{,}\) move \(4\) tic marks CW, giving \(7 = \binary{111}_{2}\text{.}\) We did not pass the tic mark at the top, so

`C`

= \(\binary{0}\text{,}\) and the result is correct.Start at the tic mark for \(5\text{,}\) move \(6\) tic marks CW, giving \(3 = \binary{011}_{2}\text{.}\) We passed the tic mark at the top, so

`C`

= \(\binary{1}\text{,}\) and the result is wrong.Start at the tic mark for \(+1\text{,}\) move \(3\) tic marks CW, giving \(-4 = \binary{100}_{2}\text{.}\) We passed the tic mark at the bottom, so

`V`

= \(\binary{1}\text{,}\) and the result is wrong.Start at the tic mark for \(-3\text{,}\) move \(3\) tic marks CCW, giving \(+2 = \binary{010}_{2}\text{.}\) We passed the tic mark at the bottom, so

`C`

= \(\binary{0}\text{,}\) and the result is wrong.Start at the tic mark for \(+3\text{,}\) move \(4\) tic marks CCW, giving \(-1 = \binary{111}_{2}\text{.}\) We did not pass the tic mark at the bottom, so

`C`

= \(\binary{0}\text{,}\) and the result is correct.