Question 1

What is two's complement and how is it computed?

Accepted Answer

Two's complement is the standard way signed integers are represented in modern CPUs. For an N-bit value, the most-significant bit (MSB) is the sign bit (0 = non-negative, 1 = negative). To negate a value you invert every bit (one's complement) and then add 1 — this is the famous 'invert and add 1' rule. The tool shows this step-by-step so you can verify e.g. that −5 in 8-bit becomes 11111011.

Question 2

What is the valid range for each bit width?

Accepted Answer

For N-bit two's complement, the representable range is −2^(N−1) … 2^(N−1) − 1. So 8-bit is −128 … 127, 16-bit is −32768 … 32767, 32-bit is −2147483648 … 2147483647, and 64-bit is −9223372036854775808 … 9223372036854775807. The tool always displays the current range and flags any input that falls outside it as an overflow.

Question 3

What is the difference between two's complement, one's complement, and sign-magnitude?

Accepted Answer

Two's complement negates by inverting all bits and adding 1 (no ±0 ambiguity, single zero). One's complement negates by inverting all bits only (so +0 = 0000 and −0 = 1111 both exist). Sign-magnitude uses the MSB as a pure sign flag and the remaining bits as a magnitude (so −5 = 1_0000101 in 8-bit, with the same ±0 ambiguity). The tool shows all three representations side-by-side so you can compare them.

Question 4

How does sign-extension work when changing bit width?

Accepted Answer

When you widen a two's-complement value, the new high-order bits are filled with copies of the original sign bit. So 8-bit 0xFB (−5) sign-extended to 16-bit becomes 0xFFFB. When you narrow, the high bits are simply dropped — if any of those dropped bits differ from the new sign bit, the value changes (overflow). The tool visualizes both directions whenever you change the width.

Question 5

What extra features does this tool have versus other two's-complement calculators?

Accepted Answer

(1) Any width from 4 to 256 bits (preset 4/8/16/32/64 or custom). (2) All three representations — two's, one's, sign-magnitude — side-by-side. (3) Step-by-step negation panel showing invert → +1. (4) Clickable bit grid: click any bit to toggle and watch the decimal value update live. (5) MSB sign bit visually highlighted. (6) Per-bit weight tooltips (2^k). (7) Hex / octal / decimal / binary views simultaneously. (8) Live range display + overflow flag. (9) Sign-extension & truncation visualizer when width changes. (10) Handles the most-negative value (−2^(N−1)) which has no positive counterpart. (11) History (localStorage, last 20). (12) Shareable URL with full state round-trip. 100% client-side and offline — your values never leave the device.

Two's Complement / Signed Integer Calculator

Two's complement

Bit grid — click any bit to toggle (MSB on left = sign bit)

All three representations side-by-side

Step-by-step negation (invert → +1)

How to use

Two's complement

Bit grid — click any bit to toggle (MSB on left = sign bit)

All three representations side-by-side

Step-by-step negation (invert → +1)

representation	binary	hex	dec
two's complement	1111 1011	FB	-5
one's complement	1111 1010	FA	-5
sign-magnitude	1000 0101	85	-5