Convert decimal integers to signed magnitude binary with clear separation of sign bit and magnitude bits
Input Decimal Integer
Bit Width
Result
Signed Magnitude
Step-by-Step Derivation
Signed Magnitude Principle
MSB = sign bit: 0 = positive, 1 = negative
Remaining bits = absolute value (magnitude)
Positive: sign bit 0 + magnitude binary
Negative: sign bit 1 + magnitude binary
Signed magnitude is the most intuitive signed integer representation: it uses one bit for sign and the rest for magnitude.
⚠8-bit signed magnitude range: -127~+127, 16-bit: -32767~+32767. Note that both +0 and -0 are valid representations.
What Is Signed Magnitude?
Signed magnitude is the simplest signed integer representation. The leftmost bit (MSB) is the sign bit (0 = positive, 1 = negative), and the remaining bits represent the absolute value of the number.
Sign Bit
The MSB is the sign bit: 0 indicates positive, 1 indicates negative. For example, 0xxxxxxx = positive, 1xxxxxxx = negative (8-bit).
Magnitude Bits
Bits after the sign bit represent the absolute value. For example, 00000101 = +5, 10000101 = -5 (8-bit).
Dual Zero
Signed magnitude has two zeros: +0 = 00000000 and -0 = 10000000. This is a major flaw of this representation.
Simple But Limited
Signed magnitude is easy to understand but impractical for computers. Arithmetic requires special handling, and two's complement is always preferred.
💡 Teaching Example: Calculate 8-bit signed magnitude of -5. Step 1: Sign is negative → sign bit = 1. Step 2: 5 in binary = 0000101 (7-bit). Step 3: Combine sign bit + magnitude → 1 0000101 → 10000101. +5 would be 00000101.
Applications
Computer Science EducationExam PreparationDigital LogicComputer HistoryNumber Systems
Frequently Asked Questions
What is signed magnitude?▼
Signed magnitude is the simplest signed integer representation: the leftmost bit (MSB) is the sign bit (0 = positive, 1 = negative), and the remaining bits represent the absolute value (magnitude).
How do you convert decimal to signed magnitude?▼
1. Determine the sign: positive = 0, negative = 1. 2. Convert the absolute value to binary. 3. Pad the binary to (bit width - 1) bits. 4. Prepend the sign bit to form the final value.
What is the range of 8-bit signed magnitude?▼
8-bit signed magnitude ranges from -127 to +127. It has two representations for zero: +0 = 00000000 and -0 = 10000000.
What are the disadvantages of signed magnitude?▼
Signed magnitude has duplicate zero representations (+0 and -0), and arithmetic circuits are more complex because addition and subtraction require separate handling. Two's complement is superior and universally adopted.
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