DSA interview question

Binary Representation and Bit Basics (Two's Complement)

Easy · Algorithms · Topics: bit manipulation

The problem

A network tool displays packet header fields as raw bits and lets engineers type bit patterns back in. You need two helpers: toBinary(n) shows the exact 32 bits a signed int is stored as, and fromBinary(s) turns a bit string (most significant bit first) back into the int. Negative numbers are the interesting part. Computers store them in two's complement, so −1 is all ones and INT_MIN is a lone sign bit. Writing these helpers exercises the basic toolkit behind every bit-manipulation problem: shifts, masks, and the difference between signed and unsigned views of the same bits.

Example: toBinary(13) → 0000 0000 0000 0000 0000 0000 0000 1101; fromBinary("1101") → 13.

Function signature

string toBinary(int n);            // exactly 32 characters, most significant bit first
int fromBinary(const string& s);   // 1 to 32 bits, most significant first; 32 bits may encode a negative

Test cases

Input	Output	Explanation
`toBinary(13)`	`0000 0000 0000 0000 0000 0000 0000 1101`	8 + 4 + 1 (spaces added for readability)
`toBinary(-1)`	`1111 1111 1111 1111 1111 1111 1111 1111`	Two's complement of −1 is all ones
`toBinary(0)`	`0000 0000 0000 0000 0000 0000 0000 0000`
`toBinary(INT_MIN)`	`1000 0000 0000 0000 0000 0000 0000 0000`	Only the sign bit
`fromBinary("1101")`	`13`
`fromBinary` of 32 ones	`-1`

(Confirm: ints are 32-bit two's complement; toBinary always returns 32 characters; fromBinary reads its input most significant bit first.)

How interviewers phrase it

"Print the 32-bit binary representation of an integer, including negatives, and convert a binary string back."
It's usually the warm-up that leads into "what do n & (n − 1) and n & −n do?"

Clarifying questions to ask

Fixed 32 bits, or the minimal representation without leading zeros?
How should negatives be shown: two's complement or a minus sign?
Which end comes first in the string? (Most significant bit first.)

Follow-ups to expect

"What is two's complement?"
"Why cast to unsigned before shifting?"
"List the core tricks."
"How many bits does a number need?"
"Complexity?"

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