Enter: check, then next. Choice questions: keys 1–4. Misses and revealed answers go into your review queue.
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Read the bits
bit: 7 6 5 4 3 2 1 0 weight:128 64 32 16 8 4 2 1
Add the weights of the 1 bits. In signed 8-bit two’s complement, replace the 128 weight with −128.
Upper four bits: 1010 0000 = 128 + 32 = 160. 1011 0000 = 128 + 32 + 16 = 176. These are unsigned readings.
Binary → hex: split into groups of four bits from the right. Hex → binary: expand each digit into four bits.
Hex digits
Two’s complement
8-bit signed range: −128 to 127. Unsigned: 0 to 255.
Decode a leading 1: unsigned value − 256. Encode a negative value: 256 + value. To negate the bit pattern: flip all eight bits and add 1, keeping eight bits.
11111111 = −1 signed or 255 unsigned. 01111111 = 127.
Operations
& both bits 1 · | either bit 1 · ^ bits differ · ~ flips bits.
&& both true · || either true · ! reverses truth. Zero is false; every nonzero value is true. Results are 0 or 1.
Left shift by k: multiply by 2k. Unsigned right shift: divide by 2k, round down. Only discard at 8 bits when the question explicitly says so.
C assumptions & type-size reference
Byte exercises use 8 bits; signed byte patterns use two’s complement. Type-size drills use the model below. These sizes are assumptions, not universal C guarantees.
| Type | Bytes in this model | Bits |
|---|---|---|
| char, signed char, unsigned char | 1 | 8 |
| short | 2 | 16 |
| int, float | 4 | 32 |
| long, long long, double, pointers | 8 | 64 |
C questions use C17 semantics and state any additional assumptions. Plain char signedness varies. Character-code questions explicitly assume ASCII. Small integer types can be promoted before arithmetic. In C, ~ and shifts do not automatically stop at eight bits.
Arithmetic right shifts are labelled as a sign-extending model; C17 leaves a negative signed right shift implementation-defined. A shift count at least as large as the promoted left operand’s width is undefined.
Language reference: WG14 C11 committee draft, §§6.3.1.1, 6.5.3, 6.5.7 and 6.5.10–14 (the relevant rules also apply in C17).