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The Payment Card
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Contents
Introduction
History: from cardboard to a computer
Lesson 0. Gates from transistors: for those who start from scratch
0.1. The idea: a transistor is a switch
0.2. Building
0.3. Check
Lesson 0 paste (Cmd+I)
Lesson 1. The ALU and register A: a calculator on switches
1.1. The idea: one action per clock
1.2. The idea: one adder for four operations
1.3. The idea: flags are the memory of the result
1.4. Building
1.5. Checking
Lesson 1 paste (Cmd+I)
Lesson 2. The program counter and ROM: lights by the program
2.1. The idea: a program is a list of commands
2.2. The idea: jumps and a subroutine
2.3. Building
2.4. Checking
Lesson 2 paste (Cmd+I)
Lesson 3. RAM from latches: a light through memory
3.1. The idea: the address is in the command
3.2. The idea: a latch writes while it is open
3.3. The idea: memory at power-on is garbage
3.4. Building
3.5. Checking
Lesson 3 paste (Cmd+I)
Lesson 4. Loops and conditions: multiplication by repeated addition
4.1. The idea: a counter down to zero
4.2. The program
4.3. Checking
Lesson 5. The IO wire and the card tester: echo
5.1. The idea: one wire for two
5.2. The idea: a byte bit by bit
5.3. The idea: the "exchange — wait" lamp
5.4. Building
5.5. Checking
Lesson 5 paste (Cmd+I)
Lesson 6. Personal data and the try counter: the card checks the PIN
6.1. The idea: the identity is in transistors
6.2. The idea: tries that are not erased
6.3. Building
6.4. Checking
Lesson 6 paste (Cmd+I)
Lesson 7. The card program: challenge-response
7.1. The idea: a secret that never leaves
7.2. The idea: a long answer in two commands
7.3. The program
7.4. Checking
Lesson 8. The card — into a chip with 8 legs
8.1. The idea: a card is what is inside
8.2. The idea: two cards — one program
8.3. Building
8.4. Checking
Lesson 8 paste (Cmd+I)
Summary
All the parts
Instructions in pictures
Lesson 4 in pictures
← Back to the lesson: Lesson 4. Loops and conditions: multiplication by repeated addition
4
Loops and conditions
no new parts: 13 × 11 by repeated addition
kh
HT-01
13 × 11
13 + 13 + … + 13 (11 times)
8b
143
A
© 2026 Daniil Khanin · khanin.info · HT-01
71
CANVAS
1
ROM
256 × 16
Memory
⬆
⬇
0801 0802 0804
0808 0810 0820
0840 0880 E011
04-mul.rom.json
1
RST
1 → 0
8b
12
pc
8b
143
A
© 2026 Daniil Khanin · khanin.info · HT-01
72
← Back to the lesson
Lesson 4. Loops and conditions: multiplication by repeated addition