How a Computer Works
How a Computer Works is a free interactive simulation from StudyFi Lab. It runs right in your browser, with no sign-up and nothing to install.
Binary numbers and a tiny CPU running instructions
Experiments
Binary numbers
A computer stores numbers as bits, 0 and 1. Each bit has a place value — a power of two: 128, 64, … 2, 1 — and the number is the sum of the place values of the bits that are on. Hexadecimal writes every 4 bits as one digit 0–F, octal every 3 bits. In two’s complement the top bit has the negative value −128, so 11111111 means −1.
Try this: Turn on all 8 bits (255), then switch to two’s complement and watch 255 become −1.
Binary addition
The numbers are added column by column from the right, just like on paper, except that 1 + 1 = 10: write 0 and carry 1 into the next column. If a carry falls out of the 8th bit, the result does not fit in 8 bits — an overflow. A computer subtracts a − b as a + (b inverted) + 1, i.e. it adds the two’s complement.
Try this: Set 200 + 100 and step through: a carry falls off the left and the result is only 44. Then try the subtraction 5 − 12.
A tiny CPU
Program and data share the same RAM. The CPU repeats three steps: fetch — copy the byte at the address in the program counter PC into the instruction register IR and increase PC; decode — the control unit works out which instruction it is; execute — carry it out, e.g. A ← A + B. The top 4 bits of a byte are the opcode, the lower 4 bits an address or a number. JZ jumps only when the flag Z = 1 (the last result was zero).
Try this: Run the “Multiply” program, then change cell 14 from 4 to 5 and check that the output ends at 15.
Frequently asked questions
What is How a Computer Works?
How a Computer Works is a free interactive simulation from StudyFi Lab. It runs right in your browser, with no sign-up and nothing to install. Binary numbers and a tiny CPU running instructions
Is How a Computer Works free?
Yes. How a Computer Works is completely free. It works in the browser on computers, tablets and phones, and you do not need an account.
What can I explore in How a Computer Works?
Binary numbers, Binary addition, A tiny CPU.
What does the “Binary numbers” experiment show?
A computer stores numbers as bits, 0 and 1. Each bit has a place value — a power of two: 128, 64, … 2, 1 — and the number is the sum of the place values of the bits that are on. Hexadecimal writes every 4 bits as one digit 0–F, octal every 3 bits. In two’s complement the top bit has the negative value −128, so 11111111 means −1.
What does the “Binary addition” experiment show?
The numbers are added column by column from the right, just like on paper, except that 1 + 1 = 10: write 0 and carry 1 into the next column. If a carry falls out of the 8th bit, the result does not fit in 8 bits — an overflow. A computer subtracts a − b as a + (b inverted) + 1, i.e. it adds the two’s complement.
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