NIELIT ECC cheat sheet

Information, Electronics and Communications Technology (IECT)

• Number systems: binary base 2, octal base 8, decimal base 10, hexadecimal base 16. Convert binary to hex by grouping 4 bits from the radix point; binary to octal by grouping 3 bits.

• Two's complement of an n-bit number = 2^n − value. Range of signed n-bit two's complement: −2^(n−1) to +2^(n−1) − 1; an n-bit unsigned range is 0 to 2^n − 1.

• Logic gates: AND (Y=A·B), OR (Y=A+B), NOT (Y=A′), NAND and NOR are universal gates; XOR (Y=A⊕B) is 1 when inputs differ, XNOR is 1 when inputs match.

• Boolean identities: A + A′ = 1, A·A′ = 0, A + AB = A, A + A′B = A + B, (A+B)(A+C) = A + BC, De Morgan: (A·B)′ = A′ + B′ and (A+B)′ = A′·B′.

• Karnaugh map grouping: group 1, 2, 4, 8 adjacent cells (powers of two), groups may wrap around edges and overlap; each group removes the variables that change within it.

• Flip-flops: SR (set-reset, invalid state when both inputs active in NOR form), JK (toggles on J=K=1), D (output follows data input, one-bit delay), T (toggles when T=1). Edge-triggered devices are the basis of registers and counters.

• Combinational vs sequential: combinational output depends only on present inputs (adders, multiplexers, decoders); sequential output depends on present inputs and stored state (counters, registers, finite state machines).

• Communications basics: Shannon capacity C = B·log2(1 + S/N); Nyquist rate for a noiseless channel = 2B samples per second; SNR in dB = 10·log10(S/N).

• Modulation: AM varies carrier amplitude, FM varies frequency, PM varies phase; digital schemes ASK, FSK, PSK, QAM combine amplitude and phase to raise bits per symbol (16-QAM = 4 bits/symbol).