How many binary bits does it take to represent 100000000000

Question

Embedded Systems Development

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Problem 1 Express equations of the following laws for AND and OR under the Boolean Logic. (1) Commutative Law; (2) Associate Law; (3) Distributive Law; (4) Identity of 0; (5) Identity of 1; (6) De Morgan's Theorem.

Problem 2 In 16 words or less give definitions of the following terms: (a) Flip-flop; (b) HiZ; (c) Open collector; (d) Tristate; e) Register; (f) Bus.

Problem 3 How many binary bits does it take to represent 100,000,000,000?

Problem 4 In the C programming language (C99), an int8_t is 8 bits, an int16_t is 16-bits, and an int32_t is 32 bits. Assuming each is signed, give the range of each type of number.

Problem 5 Each row of the following table is to contain an equal value expressed in binary, hexadecimal, and decimal. Complete the missing values. Assume each value is 8 bits and the decimal numbers are signed. The first row illustrates the process.

Binary	Hexadecimal	Decimal
01011110	0x5E	94
	0xD2
		-67
11001011
	0xE1
		79
00101010
	0xC7
		-101

Problem 6 Modify the transistor level circuit in Figure 1.13 to implement a 3-input NAND. The output will be low if and only if all three inputs are high. I.e., design it with p-type and n-type MOS transistors.

Problem 7 Using P-type and N-type transistors, design an implementation of the exclusive OR gate.

Problem 8 Suppose we will design an interface using a resistor for an LED to connect to a microcontroller. Turning on an LED requires 2 mA at 2.0 V. A digital output low (V_OL) on the microcontroller turns on the LED. That means we will utilize the negative logic. Hence, assume V_OL= 0.3V from the microcontroller. Because of the direct connection to the microcontroller, we should use 3.3V for the interface of the microcontroller to power the LED (and not 5V). Calculate the value of the resistor that could make the LED be successfully turned on.