Number Systems lesson

Skip to content

BetterDL

Learn Digital Logic without losing your mind100% free

Course Glossary About

Filter the course/

Topics

Every topic is 100% free. The first 3 need no sign-up; the rest just need a free account.

01Number SystemsBinary, hexadecimal and octal, converting between bases, binary addition and subtraction, unsigned ranges, two's complement, sign extension and overflow.No sign-up100 questions
02Boolean AlgebraBoolean variables and operators, truth tables, the laws of Boolean algebra, De Morgan's laws and step-by-step simplification.No sign-up97 questions
03Logic GatesAND, OR, NOT, NAND, NOR, XOR and XNOR: symbols, truth tables and expressions, universal gates, and reading multi-gate circuits and waveforms.No sign-up98 questions

⇧[ topics · [ outline · ] learn · \ zen

Number Systems

42 sections · 0/100 solved

Start lesson →

01Why start with numbers?
- DNumber system
02Where place value comes from: bundling
03Place value
Writing weights as powers3
The same rule in every base2
Why do computers use binary?4
Powers of 2 worth knowing2
Common mistake: weighting from the wrong end3
Adding a 0 on the right doubles3
Decimal → binary2
Common mistake: reading the remainders top-down4
Odd or even? Look at the LSB3
13Recap: binary and decimal
How much fits in n bits?6
15Why hex?
The 16 nibbles6
Common mistake: grouping from the left5
Common mistake: reading hex digits as decimal19
19Recap: hex and octal
Binary addition4
Binary subtraction4
22Recap: binary arithmetic
23Real hardware has a fixed number of bits
What about negative numbers?2
Sign-magnitude's problems1
The number wheel1
Spotting the sign at a glance2
One pattern, three meanings3
Negate: invert, then add 12
30Why does invert + 1 work?
Common mistake: inverting before padding4
Where this shows up3
Two's complement range4
Why copying the MSB works2
Where sign extension shows up1
36Recap: negative numbers
Carry out and overflow are different things2
Overflow on the number wheel1
Why comparing the two carries works1
Common mistake: "there's a carry, so it overflowed"1
41Where this shows up: status flags
42Recap

Practice exams

Practice exam 124 q
Practice exam 222 q
Practice exam 320 q
Practice exam 420 q

01 Number Systems

AND

Topic 01

Number Systems

What you'll learn

Binary, hexadecimal and octal, converting between bases, binary addition and subtraction, unsigned ranges, two's complement, sign extension and overflow.

42 sections · 100 questions · 4 practice exams

Your momentum

⚡0

in a row

🏆0

best run

📅0

day streak

3 more right on the first try for 3 in a row.

How this works

Short steps: one idea, then a question that checks it.
Get one wrong and you'll see why, with a nudge before the full solution.
This panel follows along with the idea behind each question, the key terms, and tips for that kind of question.

Shortcuts

↵: Check / continue
A–D: Pick an answer
P: Previous step
[: Topic outline
⇧[: All topics
]: Learning panel
\: Zen mode
/: Filter the outline
⌘K: Search everything

Curriculum Glossary Why this exists Terms Privacy Contact