Question 1

How does binary to decimal conversion work?

Accepted Answer

Each binary digit (bit) represents a power of 2, starting from the rightmost bit (position 0). Multiply each bit by its positional value and sum them. For 1011: (1×8) + (0×4) + (1×2) + (1×1) = 8+0+2+1 = 11. The step-by-step view shows the reverse process: repeated division by 2 with remainders read bottom-to-top.

Question 2

What is two's complement and why does it matter for negative numbers?

Accepted Answer

Two's complement is the standard way computers represent negative integers in binary. To negate a number: flip all bits, then add 1. For example, -5 in 8-bit two's complement is 11111011. This system has one representation of zero and makes arithmetic consistent — adding a negative number works the same as subtracting, so CPUs only need an adder circuit.

Question 3

Why is hexadecimal so common in programming?

Accepted Answer

One hex digit maps exactly to 4 binary bits (a nibble), and two hex digits map to one byte. This makes hex a compact, human-readable representation of binary data. Memory addresses, color codes, file format magic numbers, and byte values are all naturally expressed in hex. It's much easier to read 0xFF than 11111111 or 255 depending on context.

Question 4

What are Unix file permissions in octal?

Accepted Answer

Unix permissions have three groups (owner, group, others), each with three flags (read=4, write=2, execute=1). Summing the flags gives a digit 0-7, and three digits give the full permission. chmod 755 means owner has read+write+execute (7), group has read+execute (5), others have read+execute (5). Octal maps cleanly to these 3-bit groups.

Question 5

What is the largest value that fits in 8 bits vs 16 bits?

Accepted Answer

An unsigned 8-bit integer holds values 0–255 (2^8 - 1). A signed 8-bit integer holds -128 to +127. An unsigned 16-bit integer holds 0–65,535 (2^16 - 1), and signed holds -32,768 to +32,767. These limits explain common errors like integer overflow — for example, a counter stored in a byte will wrap from 255 back to 0 when incremented.

Binary to Decimal, Hex & Octal Converter

Binary, Octal, Decimal & Hex Converter

Related Calculators

How does binary to decimal conversion work?

What is two's complement and why does it matter for negative numbers?

Why is hexadecimal so common in programming?

What are Unix file permissions in octal?

What is the largest value that fits in 8 bits vs 16 bits?

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