Project 2: ALU

Build arithmetic circuits using the gates from Project 1.

HalfAdder

Adds two bits, outputs sum and carry.

a	b	sum	carry
0	0	0	0
0	1	1	0
1	0	1	0
1	1	0	1

let create scope (i : _ I.t) : _ O.t =
  { sum = N2t_chips.xor_ scope i.a i.b
  ; carry = N2t_chips.and_ scope i.a i.b
  }

Try it in IDE →

FullAdder

Adds three bits (two inputs + carry-in).

Hint: Chain two HalfAdders, OR the carries.

Try it in IDE →

Add16

16-bit adder. Use HalfAdder for bit 0, FullAdders for bits 1-15.

(* Ripple-carry adder *)
let sum0, carry0 = N2t_chips.halfadder_ scope a0 b0 in
let sum1, carry1 = N2t_chips.fulladder_ scope a1 b1 carry0 in
(* ... continue for all bits ... *)

Try it in IDE →

Inc16

Increment a 16-bit value by 1.

Hint: Inc16(in) = Add16(in, 1)

Try it in IDE →

ALU

The Arithmetic Logic Unit - the heart of the CPU.

Control Bits

Bit	Function
zx	if 1, set x = 0
nx	if 1, set x = NOT(x)
zy	if 1, set y = 0
ny	if 1, set y = NOT(y)
f	if 0, out = x AND y; if 1, out = x + y
no	if 1, out = NOT(out)

Output Flags

• zr = 1 if out == 0
• ng = 1 if out < 0 (MSB is 1)

Implementation Steps

(* 1. Zero x if zx *)
let x1 = N2t_chips.mux16_ scope i.x (zero 16) i.zx in

(* 2. Negate x if nx *)
let x2 = N2t_chips.mux16_ scope x1 (N2t_chips.not16_ scope x1) i.nx in

(* 3. Similarly for y... *)

(* 4. Compute both functions *)
let f_and = N2t_chips.and16_ scope x2 y2 in
let f_add = N2t_chips.add16_ scope x2 y2 in

(* 5. Select based on f *)
let out1 = N2t_chips.mux16_ scope f_and f_add i.f in

(* 6. Negate if no *)
let out2 = N2t_chips.mux16_ scope out1 (N2t_chips.not16_ scope out1) i.no in

(* 7. Compute flags *)
let ng = msb out2 in
let zr = (* out == 0 *) in

Try it in IDE →

Computing zr (zero flag)

Check if all 16 bits are 0:

(* OR all bits together, then NOT *)
let or_lo = N2t_chips.or8way_ scope (select out ~high:7 ~low:0) in
let or_hi = N2t_chips.or8way_ scope (select out ~high:15 ~low:8) in
let any_set = N2t_chips.or_ scope or_lo or_hi in
let zr = N2t_chips.not_ scope any_set

ALU Operations

With the right control bits, the ALU computes:

zx	nx	zy	ny	f	no	out
1	0	1	0	1	0	0
1	1	1	1	1	1	1
1	1	1	0	1	0	-1
0	0	1	1	0	0	x
0	0	1	1	1	1	x+1
0	0	0	0	1	0	x+y

Next Steps

• Project 3: Memory - Build sequential circuits