In base-2 notation, when the exponent increases by 1, what happens to the value?

In base-2 notation, when the exponent increases by 1, what happens to the value?

• A. The weight of the number doubles
• B. The weight halves
• C. The value increases by one
• D. The value remains the same

Answer: (A)

In binary, each position represents a power of two. When the exponent increases by one, you move to the next higher power, so that part of the value becomes twice as large. In other words, increasing the exponent multiplies that contribution by 2, and shifting a binary number left by one bit doubles its value. For example, 1011₂ is 11 in decimal, and shifting left to 10110₂ gives 22, exactly twice as much. The other ideas don’t fit: halving would happen if you moved to a lower exponent, adding one to the value is arithmetic, not exponent-based, and the value wouldn’t stay the same when you hop to a higher power.

In binary, each position represents a power of two. When the exponent increases by one, you move to the next higher power, so that part of the value becomes twice as large. In other words, increasing the exponent multiplies that contribution by 2, and shifting a binary number left by one bit doubles its value. For example, 1011₂ is 11 in decimal, and shifting left to 10110₂ gives 22, exactly twice as much. The other ideas don’t fit: halving would happen if you moved to a lower exponent, adding one to the value is arithmetic, not exponent-based, and the value wouldn’t stay the same when you hop to a higher power.