Lesson 5. The ± calculator: the minus on a lamp, the magnitude on the display

After this lesson you will have a calculator: set two numbers, choose "+" or "−" — and see a signed answer, 3 − 5 → "−" and 2. This lesson completes the kit: it already has everything a processor counts with. Lesson 6 is a bonus.

5.1. The idea: the magnitude is one more subtraction

The display can show only unsigned numbers. If we show 3 − 5 as it is, we see 254 — that is −2 in two's complement, but people do not read it that way. We need to show the sign and the magnitude separately.

The sign is the N flag, the top bit of the answer S7. The "−" lamp shows it.
The magnitude of a negative number is the same number with the opposite sign: 0 − S. And we can already subtract.

The second ADDSUB8 computes 0 + S or 0 − S, and the answer itself decides which: its S7 goes to SUB. A positive answer — the second adder adds it to zero and passes it through. A negative one — it subtracts it from zero and flips the sign.

The ± calculator for 3 − 5. The first ADDSUB8 computes S = 254 — that is −2 in two's complement, the top bit S7 = 1. S7 lights the "−" lamp and makes the second ADDSUB8 subtract: 0 − S = 2. The display shows the magnitude, the lamp shows the sign.

Set numbers from 0 to 127 (switches A7 and B7 off): in 8 signed bits there is nothing above 127. If the answer does not fit, V is lit and the display shows a wrong number.

5.2. Building

The same project. Delete the lesson 4 setup (17 switches, ADDSUB8 on the canvas, OR/NOR, NOT/AND, lamps, displays); keep Power/Ground.

The idea. The display can show only unsigned numbers. So a negative answer has to be shown as a "minus" on a lamp and the magnitude on the display. The magnitude of a negative number is the same number with the opposite sign, that is 0 − S. And we can already subtract: the second ADDSUB8 computes 0 + S or 0 − S, and the answer chooses by itself — its top bit S7 (the N flag) goes to SUB.

Set numbers from 0 to 127 (switches A7 and B7 off): in 8 signed bits there is nothing above 127. If the answer does not fit, V is lit — the display is then wrong.

Step 1. Switches and the adder A ± B

Part	Pin	Label
Input	out	A0
Input	out	A1
Input	out	A2
Input	out	A3
Input	out	A4
Input	out	A5
Input	out	A6
Input	out	A7
Input	out	B0
Input	out	B1
Input	out	B2
Input	out	B3
Input	out	B4
Input	out	B5
Input	out	B6
Input	out	B7
Input	out	SUB
ADDSUB8 (A ± B)	A0 A1 A2 A3 A4 A5 A6 A7 B0 B1 B2 B3 B4 B5 B6 B7 SUB S0 S1 S2 S3 S4 S5 S6 S7 CO V	A0 A1 A2 A3 A4 A5 A6 A7 B0 B1 B2 B3 B4 B5 B6 B7 SUB S0 S1 S2 S3 S4 S5 S6 S7 C V

Step 2. The magnitude on the display, the sign on a lamp

Part	Pin	Label
ADDSUB8 (magnitude)	A0 A1 A2 A3 A4 A5 A6 A7 B0 B1 B2 B3 B4 B5 B6 B7 SUB S0 S1 S2 S3 S4 S5 S6 S7 CO V	GND GND GND GND GND GND GND GND S0 S1 S2 S3 S4 S5 S6 S7 S7 M0 M1 M2 M3 M4 M5 M6 M7 — (free) — (free)
LED ("−" — sign)	in	S7
LED (V — does not fit)	in	V
Display	⚙	width 8, DEC, bus A
Display	⚙	width 8, DEC, bus B
Display	⚙	width 8, DEC, bus M

A0–A7 of the second adder all go to GND: that is the zero we subtract from. Its CO and V are not needed.

5.3. Check

A	Switches A7…A0	B	Switches B7…B0	SUB	Display M	Lamps	Meaning
3	0000 0011	5	0000 0101	1	2	−	3 − 5 = −2
100	0110 0100	27	0001 1011	0	127	—	100 + 27 = 127
10	0000 1010	100	0110 0100	1	90	−	10 − 100 = −90
127	0111 1111	127	0111 1111	1	0	—	127 − 127 = 0
42	0010 1010	0	0000 0000	1	42	—	42 − 0 = 42
100	0110 0100	50	0011 0010	0	—	V	150 is more than 127 — does not fit

In the "Switches" columns the top switch (A7) is on the left and A0 on the right; 1 — on, 0 — off.

If you see a big number instead of the magnitude (say 254 instead of 2), the second ADDSUB8 is not subtracting: its SUB is not on S7.

Lesson 5 paste (`Cmd+I`)

Needs ADDSUB8 from lesson 4. Delete the lesson 4 setup, keep the power.

# Lesson 5 — the ± calculator: magnitude on the display, sign on a lamp.input(A0)input(A1)input(A2)input(A3)input(A4)input(A5)input(A6)input(A7)input(B0)input(B1)input(B2)input(B3)input(B4)input(B5)input(B6)input(B7)input(SUB)ADDSUB8(A0=A0, A1=A1, A2=A2, A3=A3, A4=A4, A5=A5, A6=A6, A7=A7, B0=B0, B1=B1, B2=B2, B3=B3, B4=B4, B5=B5, B6=B6, B7=B7, SUB=SUB, S0=S0, S1=S1, S2=S2, S3=S3, S4=S4, S5=S5, S6=S6, S7=S7, CO=C, V=V)ADDSUB8(A0=GND, A1=GND, A2=GND, A3=GND, A4=GND, A5=GND, A6=GND, A7=GND, B0=S0, B1=S1, B2=S2, B3=S3, B4=S4, B5=S5, B6=S6, B7=S7, SUB=S7, S0=M0, S1=M1, S2=M2, S3=M3, S4=M4, S5=M5, S6=M6, S7=M7)led(S7)led(V)

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