Digital Design

Ang naalala ko sa digital design bukod sa napakadaming scratch paper na nasayang at every meeting madaming sinusulat lalo na kapag may quiz o exam, ay ang mga natackle namin na boolean algebra, logic gates, truth table, conversion, binary arithmetic, floating point at kung meron man akong hindi nabanggit sigro absent ako nun! Pero nung tinake ko ung subject na to halos yan lang ang ginagawa namin pati sa lab, logic nang lahat. Nag start kami sa conversion ng binary to decimal, octal, hexadecimal. Mas madli kasing magconvert kung gamit ay binary numbers. (conv). Tapos nagcomputation na kami ng bin, hex, at oct, kasi madali naman ung convertion parang recap nalang.

Binary arithmetic

Addition of binary
0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 =0, carry 1 on the next bit

Subtraction of binary
0 - 0 = 0
0 - 1 = 1, barrow 1 on the next bit
1 - 0 = 1
1 - 1 = 0

Multiplication of binary
0 x 0 = 0
0 x 1 = 0
1 x 0 = 0
1 x 1 = 1

Division of binary
*kailangan lang marunong ka ng multiplication and subtraction ng binary.


Logic gates





Truth table is a representation that helps the function of the logic gates.



Floating point arithmetic is used in computer programming to represent large numbers. The way the program represents large numbers is to raise a stated number to a certain power, or exponent. This way, larger numbers can be fed into a computer program.

Boolean algebra is a deductive mathematical system closed over the values zero and one (false and true). A binary operator “°” defined over this set of values accepts a pair of boolean inputs and produces a single boolean value.

P1: X = 0 or X = 1
P2: 0 . 0 = 0
P3: 1 + 1 = 1
P4: 0 + 0 = 0
P5: 1 . 1 = 1
P6: 1 . 0 = 0 . 1 = 0
P7: 1 + 0 = 0 + 1 = 1

T1 : Commutative Law
(a) A + B = B + A
(b) A B = B A

T2 : Associate Law
(a) (A + B) + C = A + (B + C)
(b) (A B) C = A (B C)

T3 : Distributive Law
(a) A (B + C) = A B + A C
(b) A + (B C) = (A + B) (A + C)

T4 : Identity Law
(a) A + A = A
(b) A A = A

T5 :

(a)
(b)


T6 : Redundance Law
(a) A + A B = A
(b) A (A + B) = A

T7 :
(a) 0 + A = A
(b) 0 A = 0

T8 :
(a) 1 + A = 1
(b) 1 A = A

T9 :
(a)
(b)

T10 :
(a)
(b)

T11 : De Morgan's Theorem
(a)
(b)




Reference:
http://mathworld.wolfram.com/BooleanAlgebra.html
http://www.ehow.com/how_7312481_tutorial-standard-floating-point-numbers.html