3.5 - Unit 2: Two's Complement / Fixed Point Binary / Diodes

What is -5 + 2 using 2's complement?

+5 = 01012 - Twos Compliment of 5 = 10102 + 12 = 10112 - 2 = 00102 - Result = 11012 - Find the magnitude by taking the two's compliment = 00102 + 12 = 00112 = -310

What is -2 + -6 using 2's complement?

- +2 = 00102 - Twos Compliment of 2 = 11012 + 12 = 11102 - 6 = 01102 - Twos Compliment of 6 = 10012 + 12 = 10102 - Result = 1 10002 - Discard the carry - Find the magnitude by taking the two's compliment = 01112 + 12 = 10002 = -810

Binary Addition/Subtraction using two's compliment numbers.

- If two positive numbers, the result will be positive, and no conversion necessary. - If one negative number, find the 2's complement of the positive version of the negative number and perform the addition. Discard the carry. If the result does not generate carry, then take 2's complement of the result. - If two negative numbers result in a positive, it will be called overflow. - If two positive numbers result in a negative, it will be called overflow.

What is -7 + -2 using 2's complement?

- It will result in -9 which will overflow (limit is -2N-1 = -23 = -8) - +7 = 01112, Twos Compliment of 7 = 10012 - +2 = 00102, Twos Compliment of 2 = 11102 - Result = 101112 - Drop the carry - Most significant bit is 0 which indicates positive overflow.

Convert 10111.1011 fixed point binary representation to the value representation.

23 11/16 = 23.6875

Convert 23.6875 to Fixed Point Binary Representation

23.6875 = 10111.1011

What is 101.01 represented in decimal?

5 1/4 = 5.25

Diode

A diode is a semiconductor, made silicon the element. Halfway in-between in terms of conducting and insulating. The Arrow is the Anode (positive), while the line is the Cathode (negative). Conventional current wants to flow in the direction of the arrow points.

Light Emitting Diode (LED)

A diode that will produce light when current flows through it. The point where it turns on (unless told otherwise) at 2.1V Also if not told otherwise, the diode needs 15mA of currents to be seens, and not past 25mA to blow up. 15mA-25mA, Try to design currents around 20mA

Mark Parity

A mark parity is a form of information data integrity check where the parity bit is always "marked" with the value 1. If a mark parity bit has a value of 0, an error has occurred.

Parity Bit

A parity bit is a bit that is added as the leftmost bit of a bit string to ensure that the number of bits that are 1 in it string is even or odd.

Space Parity

A space parity is a form of information data integrity check where the parity bit is always 0, otherwise, an error has occurred.

Resistor Color Code

Coding system of colored stripes on a resistor to indicate the resistor's value and tolerance.

1's Complement

Inverting bits (ex. !'s complement of 1010101 is 0101010)

2's Complement

Inverting bits and then add one to the converted bit.

Binary Coded Decimal

Restricted the numbers from 0 to 9 (0000 - 1001). We can now store those numbers as purely decimal in 4-bit entities instead of ASCII or any other coding. 2345 => 0010 0011 0100 0101.

LED

The Cathode is always on the Flat side; The Anode is on the opposite,

What is floating point binary

Where the binary number is split into a Mantissa and the Exponent. The decimal point moves.

Fixed Point Binary

Where there are a set number of bits before and after the decimal point.

None Parity

Will allow the user to only send 7 bits in a group (ex. 100 0010). The receiver knows it is only getting seven and knows what to do with that missing eight bit on its own. Basically says the user can put anything they want in that position, if the user were to send eight bits. But if the user sent seven buts that position doesn't exist.

Binary decimal point

a point placed in a binary number representation to indicate the location of the digit whose weight = 1

Even Parity

the number of 1s in the sequence adds up to an even number.

Odd Parity

the number of 1s in the sequence adds up to an odd number.

How to select Resistors

⦁ Find your Power using P = I * V in Watts. ⦁ Use Bostain's Law to find the engineering significant value. ⦁ Resistors come in 1/2 W (500 mW), 1/4th W (250 mW), and 1/8th W (125 mW). ⦁ Determine which wattage your resister can safely operate in using the above 3 types. ⦁ You CAN'T find the Wattage on the resistor, only on the package they come in. ⦁ Next, go to Standard Resistor Values, and select your 5% or 10% that most closely matches your calculated Resistance in Ω Ohms. ⦁ Next, use the resistance color selectors to find the color bands needed. ⦁ The first two bands tell you the first two significant digits in the resistance. 100 Ω would have a 1 and a 0. ⦁ The third band is the multiplier, which tells you how many more 0's you have. 100 Ω would have another 1 to indicate 1 more zero. ⦁ Look up the colors. ⦁ The fourth band is tolerance. If there is no fourth band, it could be 80% to 120% the indicated resistance. Silver is 90% to 110%, and Gold is 95% to 105%.