What is the minimum Hamming distance required in a coding scheme to detect up to 4 bit errors?
To detect up to d bit errors, the minimum Hamming distance $D_{min}$ >= d + 1 = 4 + 1 = 5.
What is the minimum Hamming distance required to CORRECT up to 3 bit errors?
To correct up to t bit errors, minimum Hamming distance $D_{min}$ >= 2t + 1 = 2(3) + 1 = 7.
The Excess-3 representation of the decimal digit 7 is:
Excess-3 of $d = d + 3$ in 4-bit binary. 7 + 3 = 10 = 1010_2.
Calculate the total number of parity bits required to construct an error-correcting Hamming code for 11 data bits.
$2^p$ >= d + p + 1. For d=11: $2^4$ = 16 >= 11 + 4 + 1 = 16. So $p = 4 parity bits$.
Which logic family provides the fastest switching speed (lowest propagation delay)?
ECL operates transistors in non-saturating mode, preventing storage delay and achieving the highest speed.