Binary To Decimal Conversion
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Practice Question
Converting 10110100 to decimal requires identifying which bit positions are 1, then summing their place values. From right to left: bit 2 (value 4), bit 4 (value 16), bit 5 (value 32), bit 7 (value 128). The sum is 4 + 16 + 32 + 128 = 180. Each bit position represents a power of 2: position 0 = 2^0 = 1, position 1 = 2^1 = 2, position 2 = 2^2 = 4, and so on up to position 7 = 2^7 = 128.
A) 164 = 10100100 in binary. This answer suggests either miscounting bit positions (reading from left instead of right) or an arithmetic error when adding 128 + 32 + 4.
C) 212 would be 11010100 in binary. This error indicates adding an extra bit value - likely including bit 6 (value 64) when it should be 0, giving 128 + 64 + 16 + 4 = 212.
D) 244 would be 11110100 in binary. This suggests multiple bit position errors, possibly adding both bit 6 (value 64) and bit 3 (value 8) incorrectly.
The most common error is reading bits from left to right instead of right to left. ALWAYS start from the rightmost bit (2^0 = 1) and work left. Another frequent mistake is using incorrect place values - write them out first: 128, 64, 32, 16, 8, 4, 2, 1. Then add only the positions with 1s.
On binary conversion questions: (1) Write place values above each bit before calculating, (2) Circle or mark bits that are 1, (3) Add only the circled values, (4) Double-check your arithmetic. The AP exam gives you time for careful work - use it! Most errors come from rushing.