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## Question:

a) Determine base xif value (211)x= (6A).16

b. Convert the followings

c. Given a tiny computer with 6 bits of word size, what are some of the smallest negative numbers and most significant positive numbers that the computer can represent in each representation?

i) One’s compliment

iii. Two’s complement

a) Take a look at the following logic diagram for a combinational system. A, B, C and D are the inputs, while Q is the output.

This circuit contains three 2-input OR gates and two 2-input OR ones.

Some logic gates can be reduced without having to alter the functionality of a circuit.

These component reductions result in a faster operating speed (less delay between input signal transition and output signal transition), reduced power consumption, lower costs, and greater reliability.

A logic diagram showing a circuit with the same function output but only two logic gates (instead five) can be constructed.

## Answer:

Locate the radix for a number

(211), x =(6A]16

The hexadecimal symbol on the right corresponds to a number that has an unknown radix.

Conversion from the hexadecimal number system to the decimal number.

What is the value of A in hexadecimal? 10

Conversion from unknown radix numbers to decimals

You can use the quadratic formula to find the roots for a=2, B=1, and C=-105.

The value for x is either 7 or 7.

The final value for the unknown is x=7

Conversion of number

OxBAD

This is a C++ or CPP value, or C value of 2989 in decimal

The value of the property is 298910

Divide consistently the decimal numbers by 3

Decimal value

The remainder values can be viewed from the bottom up.

A word size limit of 6 bits

Largest positive (3110): 0111112

Largest positive (3110): 0111112

Logic diagram for a circuit with the same function output but only two logic gates as opposed to five.

The output Q of inputs A B C is the following expression. It is simplified as follows:

Boolean algebra simplification

Boolean Algebra states that as long there is a high, then the output is high.

If both inputs and output are low, then the output is high.

This is the complement rule in the OR operator.

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