Convert decimal integers to one's complement binary representation with detailed bit-flipping steps
Input Decimal Integer
Bit Width
Result
One's Complement
Step-by-Step Derivation
One's Complement Principle
Positive: one's complement = normal binary
Negative: flip all bits of absolute value
Sign bit: 0 = positive, 1 = negative
Has two representations for zero (+0 and -0)
One's complement is an early method for representing signed integers. While less common today, it teaches important concepts about binary arithmetic.
⚠8-bit one's complement range: -127~+127, 16-bit: -32767~+32767. Note that both +0 and -0 have valid representations.
What Is One's Complement?
One's complement is a signed integer representation. Positive numbers are stored as normal binary. Negative numbers are formed by flipping all bits of the positive equivalent. The leftmost bit (MSB) is the sign bit: 0 for positive, 1 for negative.
Positive Numbers
Positive one's complement is identical to normal binary. For example, +5 in 8-bit one's complement = 00000101.
Negative Numbers
Negative one's complement flips all bits of the absolute value. For example, -5 = ~5 = 11111010 (8-bit).
Dual Zero
One's complement has +0 = 00000000 and -0 = 11111111. This is a major flaw of the system.
Arithmetic
One's complement addition requires end-around carry (carry-out is added back in). Two's complement doesn't need this.
💡 Teaching Example: Calculate 8-bit one's complement of -5. Step 1: 5 in binary = 00000101. Step 2: Flip all bits: 0→1, 1→0. Result: 11111010. Note that one's complement of 11111010 is 00000101, returning to +5.
One's complement is a signed integer representation where positive numbers are the same as binary, and negative numbers are formed by flipping all bits of the positive counterpart. It has both +0 and -0 representations.
How do you calculate one's complement?▼
For positive numbers: one's complement equals the normal binary representation. For negative numbers: take the absolute value, convert to binary, pad to desired bit width, then flip all bits (0→1 and 1→0).
What is the range of 8-bit one's complement?▼
8-bit one's complement ranges from -127 to +127. The two zero representations are 00000000 (+0) and 11111111 (-0).
What are the disadvantages of one's complement?▼
One's complement has two representations of zero (+0 and -0), which complicates comparisons and arithmetic. It also requires end-around carry for subtraction. Two's complement is more widely used today.
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