Bases 2, 8 and 16
Positional notation and conversions of natural numbers between decimal, binary, octal and hexadecimal: successive divisions, sum of weights, grouping by 3 and 4 bits, the 0b, 0o and 0x prefixes.
- 25 cards
- 7 topics
- Free
The outline, topic by topic
Each topic is weighted the way the exam weighs it.
- Concepts
- Questions
- Sort and link
- On the timeline
- The numbers
- Scenarios
- Understand
A few cards from the deck
Positional notation: what is it?
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A way of writing numbers where the value of each digit depends on its place: it is multiplied by the power of the base that matches that place.
In base 10, 305 is 3 × 100 + 0 × 10 + 5 × 1. In base 2, 101 is 1 × 4 + 0 × 2 + 1 × 1 = 5. The place matters as much as the digit.
What is the binary form of 45?
- 101101
- 101011
- 110101
- 101110
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101101
45 = 32 + 8 + 4 + 1, so the weights 32, 8, 4 and 1 are set to 1: 101101. The other three are 43, 53 and 46.
In a binary number, the leftmost bit is the … significant bit and the rightmost one is the … significant bit.
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In a binary number, the leftmost bit is the most significant bit and the rightmost one is the least significant bit.
In 1000 0001, the left bit weighs 128 and the right one 1: changing the first alters the value far more than changing the second.
Binary: what is it?
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The base-2 numeral system, whose only digits are 0 and 1 and whose weights are 1, 2, 4, 8, 16…
It is the machine's base: a digital circuit tells only two voltage levels apart. 173 is written 10101101, because 128 + 32 + 8 + 4 + 1 = 173.