Today is our last day of non-review discussion of bits, number storage, boolean logic, and circuits. After the midterm, you’ll next see these topics in the Computer Hardware class.
Midterm:
- One week from today
- In this classroom
- On paper
- Bring a pencil, notes on paper, and an internet-disconnected calculator if you have one.
- We’ll review midterm topics on Monday.
Today: Sketching the rest of a CPU
We have:
- A circuit that adds two numbers (an adder).
- A circuit that can store a number (a register).
- For today’s exercise, let’s say “a number” is 16 bits.
We need:
- Arithmetic Logic Unit
- An adder
- A subtracter (this is just an adder, but we two’s complement the second number before adding).
- A multiplier
- Whatever other operations
- Circuitry to activate only one operation.
- So we have three inputs and one output:
- operation
- input A
- input B
- output
- Register file
- A bunch of registers (say, 8)
- Circuitry to select a single register
- Circuitry to read the selected register
- Circuitry to write the selected register
- A memory
- This is just a big register file. Instead of having 8 registers, we have 64k or 100 million or something.
- Typically we do byte addressing, but we could do 16 bit word addressing to make our story simpler right now.
- A CPU
- Our CPU reads a fixed size instruction from memory at the address specified by a reserved register (the “program counter”).
- Then it executes that instruction.
- The first few bits are a number specifying which instruction.
- The next specify what the instruction operates on (e.g. which registers).
- The instruction reads some input registers, writes an output register, uses the ALU, maybe does something with RAM.
- Then the CPU increments the program counter and reads the next instruction, repeating forever.
Example:
- Instructions are 16 bits.
- The first 7 bits specify which instruction.
- The remaining 9 bits specify three registers: inputs A, B and output.
- So ADD, r0 + r1 => r2 might be 0000 000 000 001 010
- Can we really do this in one clock cycle?
- What if one of the input registers is also the output register?
More complex example:
- Let’s write a computer program that determines how many bits are set in a number.
- Our computer is really simple - you punch in a number on a keypad which is shown on a numeric display showing the value of register 0. You press the RUN button, the stored program runs, and the single number output is whatever is in register 0 when it’s done.
- The stored program lives at memory address 0x100 (256).
r1 = 0
while r0 > 0:
if r0 & 1 != 0:
r1 += 1
r0 = r0 / 2
r0 = r1
