Binary Addition

Two pairs of buttons are used as 2-bit inputs. So btns(3:2) and btns(1:0) form two inputs with the integer range 0 to 3. They are then added together to create a 3-bit output displayed as leds(2:0). The logic is crafted to produce the following table of results.

Integer:

btns(3:2)	btns(1:0)	leds(2:0)
0	0	0
0	1	1
0	2	2
0	3	3
1	0	1
1	1	2
1	2	3
1	3	4
2	0	2
2	1	3
2	2	4
2	3	5
3	0	3
3	1	4
3	2	5
3	3	6

Binary:

btns(3:2)	btns(1:0)	leds(2:0)
“00”	“00”	“000”
“00”	“01”	“001”
“00”	“10”	“010”
“00”	“11”	“011”
“01”	“00”	“001”
“01”	“01”	“010”
“01”	“10”	“011”
“01”	“11”	“100”
“10”	“00”	“010”
“10”	“01”	“011”
“10”	“10”	“100”
“10”	“11”	“101”
“11”	“00”	“011”
“11”	“01”	“100”
“11”	“10”	“101”
“11”	“11”	“110”

Equations

\[\begin{aligned} \mathtt{led}(0) &= \mathtt{btns}(2) \oplus \mathtt{btns}(0) \\ \mathtt{led}(1) &= (\mathtt{btns}(2) . \mathtt{btns}(0)) \oplus \mathtt{btns}(3) \oplus \mathtt{btns}(1) \\ \mathtt{led}(2) &= (\mathtt{btns}(3) . \mathtt{btns}(1)) + (\mathtt{btns}(3) \oplus \mathtt{btns}(1)) . \mathtt{btns}(2) . \mathtt{btns}(0) \\ \end{aligned}\]

Circuit