From gates to a processor

Wire one gate's output into another gate's input and you get a circuit. Work a circuit out row by row, each gate using only what arrives on its wires, then build circuits to match truth tables, even from NAND gates alone.

1. OR, then NOT
2. Try: follow the wires
3. Worked example: row by row › Gate by gate (A = 1, B = 1)
4. Worked example: row by row › Find the mistake
5. Worked example: row by row › Name it
6. Vary: build to a table › NAND
7. Vary: build to a table › A and not B
8. Vary: build to a table › NOT from NAND
9. Vary: build to a table › OR from NAND
10. Practise: read the circuit › NOT then AND
11. Practise: read the circuit › NAND then NOT
12. Practise: read the circuit › Review: rows
13. Build XOR

Adding two bits is a truth table: the sum is XOR and the carry is AND, a half adder. A full adder also takes a carry in. One full adder per place, carries passed to the left, adds whole binary numbers.

1. 1 + 1
2. Try: build a half adder
3. Worked example: 5 + 7 in four bits › Place by place
4. Worked example: 5 + 7 in four bits › Find the mistake
5. Worked example: 5 + 7 in four bits › Why three inputs?
6. Vary: carries › No carry
7. Vary: carries › One carry
8. Vary: carries › Overflow
9. Vary: carries › Every place
10. Practise: adders › Add
11. Practise: adders › How many adders?
12. Practise: adders › Review: overflow
13. Build a full adder

Feed two gates' outputs back into each other and they hold a bit: a latch. Set makes it 1, Reset makes it 0, and with both off it keeps what it had. Latches side by side make a register that stores a number.

1. On, then off
2. Try: set it and let go
3. Worked example: the latch's rules › Four settings
4. Worked example: the latch's rules › Find the mistake
5. Worked example: the latch's rules › Why RAM forgets
6. Vary: latches and a register › Reset
7. Vary: latches and a register › Both on
8. Vary: latches and a register › Store a number
9. Vary: latches and a register › Keep it
10. Practise: memory › Register size
11. Practise: memory › RAM in bits
12. Practise: memory › Review: RAM and storage
13. Hold a number

A processor repeats one cycle: fetch the instruction the program counter points at, decode it, execute it, one step per clock tick. The program is numbers in the same memory as the data. Step a tiny processor, change its program, and write your own.

1. What will it output?
2. Try: tick by tick
3. Worked example: one instruction, three ticks › LOAD 6, tick by tick
4. Worked example: one instruction, three ticks › Find the mistake
5. Worked example: one instruction, three ticks › Clock speed
6. Vary: change the program › Change the data
7. Vary: change the program › Change an instruction
8. Vary: change the program › Store the answer
9. Vary: change the program › A loop
10. Practise: the cycle › The PC
11. Practise: the cycle › Loops
12. Practise: the cycle › Review: adding
13. Write a program