Binary Conversions and K-Map Boolean Simplification
Classified in Electronics
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Sure! Here are the conversions you requested:
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(10000101)2 to hexadecimal (base 16):
- Group the binary digits in sets of four from the right: 1000 0101
- (1000)2 = 8, (0101)2 = 5
- Therefore, (10000101)2 = (85)16.
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(AA)16 to decimal (base 10):
- A = 10 in decimal, so (AA)16 = 10 × 161 + 10 × 160 = 160 + 10 = 170.
- Therefore, (AA)16 = (170)10.
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(5.5)10 to binary (base 2):
- The integer part: 5 = (101)2.
- The fractional part: 0.5 = (0.1)2.
- Combine them: (5.5)10 = (101.1)2.
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2's complement of (01001)2:
- Invert the digits: (01001)2 → (10110)2.
- Add 1: (10110)2 + (00001)2 = (10111)2.
- Therefore, the 2's complement of (01001)2 is (10111)2.
Simplify F(A, B, C, D) with a K-Map
To simplify the Boolean expression F(A, B, C, D) = Σ m(0, 2, 3, 8, 10, 11, 12, 14) using a Karnaugh... Continue reading "Binary Conversions and K-Map Boolean Simplification" »