What is the hexadecimal representation of the binary number 110101110010_2?
Group bits into nibbles (4 bits) from right to left: 1101 = D (13), 0111 = 7, 0010 = 2. Hexadecimal value = D72_16.
In 8-bit 2's complement representation, what decimal value does the binary string 11110100 represent?
Since MSB is 1, it is negative. Take 2's complement: 1's complement of 11110100 = 00001011. Add 1 = 00001100 = 12. Thus, decimal value is -12.
Why is Gray code extensively used in rotary optical encoders?
Gray code is a unit-distance unweighted code where consecutive numbers differ by only a single bit, preventing switching errors in mechanical/rotary encoders.
Convert binary 1011_2 to its equivalent Gray code.
MSB remains same G3 = B3 = 1. G2 = B3 XOR B2 = 1 XOR 0 = 1. G1 = B2 XOR B1 = 0 XOR 1 = 1. G0 = B1 XOR B0 = 1 XOR 1 = 0. Gray code = 1110.
What is the maximum valid 4-bit combination in standard Binary Coded Decimal (BCD)?
BCD represents single decimal digits (0-9) using 4 bits. Valid range is 0000 (0) to 1001 (9). Values 1010 to 1111 are invalid.