GCE Advanced Level ICT

Wednesday, October 9, 2013

Two's Complement Binary Addition

-39 + 92 = 53:

1	1		1	1
	1	1	0	1	1	0	0	1
+	0	1	0	1	1	1	0	0
	0	0	1	1	0	1	0	1

Carryout without overflow. Sum is Correct.

104 + 45 = 149:

	1	1		1
	0	1	1	0	1	0	0	0
+	0	0	1	0	1	1	0	1
	1	0	0	1	0	1	0	1

Overflow, no carryout. Sum is not correct.

10 + -3 = 7:

1	1	1	1	1
	0	0	0	0	1	0	1	0
+	1	1	1	1	1	1	0	1
	0	0	0	0	0	1	1	1

Carryout without overflow. Sum is correct.

-1 + 1 = 0:

1	1	1	1	1	1	1	1
	1	1	1	1	1	1	1	1
+	0	0	0	0	0	0	0	1
	0	0	0	0	0	0	0	0

Carryout without overflow. Sum is correct.

Boolean Expression Simplification

Simplify: C + BC:

Expression Rule(s) Used

C + BC Original Expression

C + (B + C) DeMorgan's Law.

(C + C) + B Commutative, Associative Laws.

T + B Complement Law.

T Identity Law.

Simplify: AB(A + B)(B + B):

Expression	Rule(s) Used
AB(A + B)(B + B)	Original Expression

AB(A + B)	Complement law, Identity law.
(A + B)(A + B)	DeMorgan's Law
A + BB	Distributive law. This step uses the fact that or distributes over and. It can look a bit strange since addition does not distribute over multiplication.
A	Complement, Identity.

Simplify: (A + C)(AD + AD) + AC + C:

Expression	Rule(s) Used
(A + C)(AD + AD) + AC + C	Original Expression

(A + C)A(D + D) + AC + C	Distributive.
(A + C)A + AC + C	Complement, Identity.
A((A + C) + C) + C	Commutative, Distributive.
A(A + C) + C	Associative, Idempotent.
AA + AC + C	Distributive.
A + (A + T)C	Idempotent, Identity, Distributive.
A + C	Identity, twice.

You can also use distribution of or over and starting from A(A+C)+C to reach the same result by another route.

Simplify: A(A + B) + (B + AA)(A + B):

Expression	Rule(s) Used
A(A + B) + (B + AA)(A + B)	Original Expression

AA + AB + (B + A)A + (B + A)B	Idempotent (AA to A), then Distributive, used twice.
AB + (B + A)A + (B + A)B	Complement, then Identity. (Strictly speaking, we also used the Commutative Law for each of these applications.)
AB + BA + AA + BB + AB	Distributive, two places.
AB + BA + A + AB	Idempotent (for the A's), then Complement and Identity to remove BB.
AB + AB + AT + AB	Commutative, Identity; setting up for the next step.
AB + A(B + T + B)	Distributive.
AB + A	Identity, twice (depending how you count it).
A + AB	Commutative.
(A + A)(A + B)	Distributive.
A + B	Complement, Identity

Basic Logic Gates Problems

Draw a logic circuit for (A + B)C.
Draw a logic circuit for A + BC + D.
Draw a logic circuit for AB + AC.
Draw a logic circuit for (A + B)(C + D)C.

Source : http://sandbox.mc.edu

Thursday, August 1, 2013

IPV4 Sub netsTutorial

Start > CMD > ipconfig

IPV6 Addresses was introduced to provide large address space

IPv6 Testing Tools

Check your IPv6 address formatting is correct

Check if the IPv6 address you are using is valid and properly formatted IPv6

Check your IPv6 connectivity from this website (Sydney)

Check your IPv6 connectivity from ipv6-test.com (USA)

Check Internet Service Provider IPv6 readiness

For full IPv6 connectivity, service providers need to set up IPv6-addressed nameservers, AAAA ('quad-A') address records, AAAA mail exchange records and allow website access over IPv6.

Check your IPv6 Path Maximum Transmission Unit

If a host sends IPv6 packets that are too big for part of its route, it should get a Packet Too Big message so it can re-transmit the data in smaller packets. If that message doesn't get back (e.g. firewalls, mis-configured routers) it can affect IPv6 connectivity.

Expression	Rule(s) Used
C + BC	Original Expression

C + (B + C)	DeMorgan's Law.
(C + C) + B	Commutative, Associative Laws.
T + B	Complement Law.
T	Identity Law.

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