Signed Binary to Decimal Converter
2's Complement Support
Convert signed binary numbers to decimal using 2's complement interpretation. Understand how computers represent negative numbers — with automatic sign detection and step-by-step breakdowns.
5Number Systems
∞Precision
0msLatency
Interactive Tool Module
Visualizing 2's Complement Sign Flips
In 8-bit signed binary architectures, clicking a bit flips it (1's complement). To negate a binary number entirely natively representing it negatively, you flip **all** bits, and automatically add `1`. Try it below.
8-Bit Memory Register
Signed Decimal Evaluation
40
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FAQ
Frequently Asked Questions
What is signed binary?
Signed binary is a way of representing both positive and negative integers in binary. The most common method is 2's complement, where the most significant bit (MSB) acts as the sign bit: 0 for positive, 1 for negative. For example, in 8-bit signed binary, 11111110₂ = -2₁₀.
What is 2's complement?
2's complement is the standard method computers use to represent signed integers. To find the 2's complement (negative) of a binary number: invert all bits (1's complement), then add 1. For example, to represent -5 in 8 bits: 5 = 00000101, invert → 11111010, add 1 → 11111011₂ = -5₁₀.
How do you convert signed binary to decimal?
If the MSB is 0, convert normally (it's positive). If the MSB is 1, the number is negative: either (a) invert all bits, add 1, convert to decimal, then negate; or (b) use the formula: value = -(2ⁿ) + (unsigned value), where n is the bit width. Example: 11111011₂ (8-bit) = -128 + 123 = -5₁₀.
What is the range of signed binary numbers?
For an n-bit signed binary number in 2's complement, the range is from -2ⁿ⁻¹ to 2ⁿ⁻¹ - 1. For 8 bits: -128 to 127. For 16 bits: -32,768 to 32,767. For 32 bits: -2,147,483,648 to 2,147,483,647. The negative range has one extra value because zero uses a positive bit pattern.
Why do computers use 2's complement?
2's complement simplifies hardware design because addition and subtraction use the same circuit. There is only one representation of zero (unlike sign-magnitude or 1's complement). The overflow behavior is also predictable, making arithmetic simpler for CPU designers.
What is the difference between signed and unsigned binary?
In unsigned binary, all bits represent magnitude, so values range from 0 to 2ⁿ-1. In signed binary (2's complement), the MSB represents the sign, giving a range of -2ⁿ⁻¹ to 2ⁿ⁻¹-1. For example, the 8-bit pattern 11111111 is 255 unsigned but -1 signed.
How does sign extension work?
Sign extension is the process of increasing the number of bits while preserving the sign and value. You copy the sign bit (MSB) into all new higher-order bits. For example, extending 1011₂ (-5 in 4-bit) to 8 bits gives 11111011₂, which is still -5. Positive numbers get padded with 0s.