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Unsigned To Signed Radix Converter

Convert unsigned binary numbers to signed representations with sign-magnitude, ones complement, and twos complement

Unsigned Binary Number

Signed Number Representations

① Sign-Magnitude: leftmost bit = sign, rest = magnitude

② Ones Complement: invert all bits to negate

③ Twos Complement: invert bits + 1 to negate

Three common ways to represent signed binary numbers: sign-magnitude (simplest), ones complement, and twos complement (most practical).

⚠ Make sure your binary number has enough bits. The leftmost bit becomes the sign bit in all three representations.

What Are Signed Number Representations?

Signed number representations extend binary to handle negative values using different encoding schemes.

Sign-Magnitude

Leftmost bit: 0 = positive, 1 = negative. Remaining bits = absolute value. Simple but has two zeros (0000 and 1000).

Ones Complement

Negative = invert all bits of positive. Still has two zeros. Addition requires end-around carry.

Twos Complement

Negative = invert bits + 1. Single zero, same addition for signed/unsigned. Used in all modern computers.

Bit Length Matters

Signed representations depend on bit length. 4-bit 1010 ≠ 8-bit 1010. More bits = larger range.

💡 Teaching Example: 4-bit 1010. Sign-magnitude: -2. Ones complement: -5. Twos complement: -6. Same bits, different values depending on representation!

Applications

Computer Architecture Digital Logic Microprocessors Assembly Language Computer Science

Frequently Asked Questions

What is the difference between unsigned and signed numbers?▼

Unsigned numbers only represent zero and positive values. Signed numbers can represent positive, zero, and negative values using special encoding schemes like sign-magnitude, ones complement, or twos complement.

What is sign-magnitude representation?▼

Sign-magnitude uses the leftmost bit as a sign bit (0 = positive, 1 = negative), with the remaining bits representing the magnitude (absolute value). Simple but has two representations for zero.

How does twos complement work?▼

Twos complement is the most common signed representation. To negate: invert all bits (ones complement) then add 1. Only one zero, and addition/subtraction work the same as unsigned.

Why is twos complement preferred?▼

Twos complement has a single zero representation, simplifies hardware design, and allows using the same addition/subtraction circuits for both signed and unsigned numbers.

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