Digital Logic

Decimal to Binary

Divide by 2, 0 = 0, 0.5 = 1

Binary to Decimal

Column Weights by 2

Decimal to Hexadecimal

Divide by 16, Rem is Hex equiv.

Hexadecimal to Decimal

Column Weights by 16

Hexadecimal to Binary

Replace Digits with Binary equiv. 16

Binary to Hexadecimal

Group by 4, Convert

Octal to Decimal

Column Weights by 8

Decimal to Octal

Divide by 8, Rem is Octal equiv.

Binary to Octal

Group by 3, Convert

Octal to Binary

Replace Digits with Binary equiv. 8

Single Precision FP

Sign (1), Exponent (8), Fraction (23)

Single Precision Exponent

2^(y-127)

Double Precision FP

Sign (1), Exponent (11), Fraction (52)

Double Precision Exponent

2^(y-1023)

AND Gate

produces HIGH Out only if all In are HIGH

OR Gate

produces HIGH Out if any In is HIGH

NOT Gate

produces inverted Out, HIGH = LOW and LOW = HIGH

NAND Gate

produces LOW Out if all In are HIGH

NOR Gate

produces LOW Out if any In are HIGH

XOR Gate

produces HIGH Out if all In are at Opposite Logic Levels

XNOR Gate

produces HIGH Out if all In are identical

Truth Table Variables

2^n where n = number of variables, Sequence in unit Binary

Minterms

Standard Products

Maxterms

Standard Sums

Operator Precedence

Parentheses, Not, And, Or

Commutative

A + B = B + A, AB = BA

Associate

A + (B + C) = (A + B) + C, A(BC) = (AB)C

Distributive

AB + AC = A(B + C)

Complement

AA’ = 0, A + A’ = 1

Identity

A \* 1 = A, A + 0 = A

Null Elements

A \* 0 = 0, A + 1 = 1

Idempotence

AA = A, A + A = A

Demorgan’s Theorem 1

/A/B = /A + /B

Demorgan’s Theorem 2

/(A + B) = /A \* /B