C-03 — Number Systems and Digital Devices

Which field of study are modern computers and electronic gadgets based upon?

Digital electronics relies on which mathematical structure?

The Piraha indigenous tribe of Brazil can count only up to which number?

The need for accounting and counting large numbers crept up on humans mainly after they learned—

The Sumerian-Babylonian number system was based on which number?

The Egyptian number system was based on which number?

Traces of the 60-based number system are still found in our—

The Mayan number system was based on which number?

Who were the first people to use zero as a number in their system?

The Indian number system used how many separate symbols to express all numbers (including zero)?

The symbols 1, 2, 3 ... that we use today are known as—

Consider the following statements about ancient number systems: Which of the following is correct?

Which number systems gained popularity in the modern age besides the decimal system?

Which of the following best defines a number system?

Number systems are classified into which two types?

In which number system does a symbol keep the same value regardless of its position?

Roman numerals are an example of which type of number system?

In the number 555 (decimal), what value does the leftmost 5 represent?

In a positional number system, the value of a digit depends on—

In a 16-based positional system, each position from right to left increases the local value by multiples of—

Consider the following statements: Which of the following is correct?

Why is the binary number system preferred for digital devices over the decimal system?

The binary number system uses how many symbols?

What is the base (radix) of the binary number system?

What is the only limitation of the binary number system mentioned in the text?

In the binary number system the local values increase with multiples of—

In binary numbers, MSB and LSB stand for—

What is the decimal value of the binary number $(11001.110)_2$?

The number of digits needed in a number system is referred to as its—

What is the base of the octal number system?

Which set of digits is used to express octal numbers?

What is the base of the hexadecimal number system?

In hexadecimal, the digits consist of 0 to 9 and which letters?

How many binary bits are needed to express one hexadecimal digit?

The decimal number 16 is written in hexadecimal as—

Convert the binary number $(101101)_2$ to decimal.

To convert a binary number to decimal, we multiply each bit by its local value which is a multiple of—

Convert the decimal number $25$ to binary.

In the repeated-division method of decimal-to-binary conversion, the remainders read from last to first give the bits from—

To convert a decimal number to any base, in the repeated-division method we divide by—

Convert the decimal number $37$ to binary.

When converting a decimal fraction to binary, we repeatedly multiply the fraction by—

Convert the decimal number $710$ to octal.

When converting a decimal fraction to octal, we repeatedly multiply the fraction by—

Convert the octal number $(123.45)_8$ to decimal.

To convert octal to decimal we multiply each digit by $8^n$, where $n$ is—

Each octal digit can be expressed using how many binary bits?

Convert the octal number $(412)_8$ to binary.

When converting binary to octal, the binary digits are grouped (from LSB) into groups of—

Convert the binary number $(10100101011)_2$ to octal.

Convert the hexadecimal number $(356)_{16}$ to decimal.

Convert the hexadecimal number $(2AF)_{16}$ to decimal.

When converting hexadecimal to decimal, the multipliers used are powers of—

Hexadecimal to binary conversion uses how many binary bits per hexadecimal digit?

Convert the hexadecimal number $(9F23)_{16}$ to binary.

When converting binary to hexadecimal, the bits are grouped into groups of—

Convert the binary number $(10110111000011)_2$ to hexadecimal.

What is the easiest way to convert from octal to hexadecimal or vice versa?

Convert the hexadecimal number $(B2F)_{16}$ to octal.

Why does an electronic circuit performing binary addition need to know the number of bits, while manual addition does not?

In reality, a digital device needs only how many basic circuits to perform all arithmetic operations?

The two essential circuits needed for all arithmetic in a digital device are—

In a digital device, multiplication is performed by—

Perform the binary addition: $(101100101)_2 + (11001001)_2$.

In the straightforward signed-number representation, which bit is reserved for the sign?

In signed representation, a sign bit of 0 indicates the number is—

How is the decimal number $+1$ written as an 8-bit signed number?

How is the decimal number $-1$ written as an 8-bit signed number (sign-bit method)?

Using the 4-bit sign-bit method, decimal $-2$ is represented as—

What serious problem arises in the simple sign-bit method of representing signed numbers?

In the 4-bit sign-bit method, the values 0000 and 1000 represent—

According to the text, a negative number is one which—

How is the 1's complement of a binary number obtained?

How is the 2's complement of a binary number obtained?

The 1's complement of 10110011 is—

The 2's complement of 10110011 is—

Taking the 2's complement of a number twice gives—

In the 2's complement system, how do we decide whether a binary number is positive or negative?

The 2's complement of the 4-bit number 1001 is—

The 4-bit 2's complement representation of $-6$ is—

The 8-bit 2's complement representation of $-83$ is—

Using 2's complement to subtract $25$ from $50$, the overflow (9th) bit in the result must be—

Subtract $(25)_{10}$ from $(50)_{10}$ using the 2's complement method. The result is—

Subtract $(50)_{10}$ from $(25)_{10}$ using the 2's complement method. The result is—

Consider the following statements about 2's complement: Which of the following is correct?

The conversion of characters, letters, words and symbols into a binary system is known as—

Why must characters and symbols be converted to 0s and 1s?

What does BCD stand for?

In BCD, each decimal digit is expressed using how many binary bits?

In BCD, which six binary combinations are never used?

How is the decimal number 10 expressed in BCD?

Express the decimal number 4578 in BCD.

The BCD code 1001 0010 0110 represents which decimal number?

In an alphanumeric code, one can use—

What does EBCDIC stand for?

EBCDIC is an 8-bit code, so it can express how many different symbols?

Which company first used the EBCDIC coding mechanism?

What does ASCII stand for?

ASCII is originally a code of how many bits?

As a 7-bit code, how many different symbols can standard ASCII express?

In ASCII, the first 32 codes are used as—

According to the ASCII table, the symbol for code number 65 is—

According to the ASCII table, the decimal code for the capital letter 'Z' is—

The 8-bit version of ASCII with another 128 symbols is known as—

Unicode is an encoding system that acts on—

Which organization launched the first version of Unicode?

The first version 1.0.0 of Unicode was launched in which year?

The 13th edition of Unicode launched in 2020 supports how many languages?

In the UTF-8 format, a character is represented using how many bytes?

In Unicode, the code $0041_{16}$ represents which character?

UTF-16 is a unit of how many bits?

UTF-32 represents each character within how many bytes?

Which Unicode format has become the unwritten standard for use on websites?

Using the default 16-bit encoding, how many codes can Unicode generate?

Consider the following statements about codes: Which of the following is correct?

Boolean Algebra works with which values only?

Boolean Algebra has which three mathematical operations?

According to Boolean addition, $1 + 1 = ?$

According to Boolean multiplication, $1 \cdot 1 = ?$

What is the correct order of operations in Boolean Algebra?

Evaluate the Boolean expression $1 \cdot 0 + ((0+1))$ following Boolean rules. (Note: the overbar denotes complement.)

In a digital device, the values 0 and 1 in Boolean algebra actually represent—

Which Boolean theorem is expressed as $x + x = x$ and $x \cdot x = x$?

The theorem $x + 0 = x$ and $x \cdot 1 = x$ is known as the—

The Domination theorem states that—

Which theorem is represented by $x + xy = x$ and $x(x+y) = x$?

De Morgan's theorem states that—

The distributive theorem $x + yz = (x+y)(x+z)$ is proved using which theorems during simplification?

Simplify the Boolean expression $xyz + xy + x$.

Simplify the Boolean expression $xy\bar{z} + \bar{x}\bar{y}\bar{z} + xyz + \bar{x}\bar{y}z$.

A table that expresses the relationship between every possible input and output is called a—

If there are $n$ variables, how many different input combinations will the truth table have?

A truth table with two variables will have how many input rows?

For the expression $x \cdot (\overline{y+z})$, the output is 1 only when—

Electronic devices that can express Boolean logic are called—

The complement operation in Boolean algebra is performed by which gate?

The multiplication operation in Boolean algebra is performed by which gate?

The addition operation in Boolean algebra is performed by which gate?

To get a 1 output from an AND gate, the inputs must be—

An OR gate produces a 1 output when—

Why are AND, OR and NOT called basic gates?

For the circuit expressing $x(\overline{y+z})$, if $x=1, y=0, z=1$, the output is—

In a circuit that simulates a voting system where 2 out of 3 people voting 'yes' wins, the output expression is—

A NAND gate is equivalent to which combination?

A NOR gate is equivalent to—

Which two gates are called universal gates?

Why are NAND and NOR called universal gates?

The basis for stating that any Boolean operation can be done using only complement-and-addition or complement-and-multiplication comes from which theorem?

Consider the following statements about universal gates: Which of the following is correct?

Which gate is used to perform 1-bit binary addition (the result bit)?

An XOR gate produces a 1 output when—

The Boolean expression of an XOR gate is—

An XNOR gate can be made by—

For an XNOR gate, the output is 1 when—

Why can't the AND gate be used to add two binary numbers like the XOR gate?

In a half adder circuit, the carry bit is obtained using which gate?

Why is a half adder circuit called "half"?

A full adder circuit adds how many bits at a time?

In a full adder, what does COUT represent?

The simplified expression for $C_{OUT}$ of a full adder is—

In a half adder truth table, the sum (S) is 1 only when—

When adding four bits with full adders, why is a fifth bit needed?

In the first full-adder block when adding two numbers, why is CIN1 = 0?

A flip-flop is a memory element that can store how many binary bits?

A flip-flop has how many permanent states?

The external signal that changes a flip-flop from one state to another is called a—

A flip-flop is also known as—

A flip-flop generally has two outputs where—

Flip-flops are mostly used as—

A register is a set of—

An n-bit register consists of how many flip-flops?

Placing new data into a register is called—

Who can store information in CPU registers?

Registers are widely used as—

A counter is a sequential circuit that can—

A counter is a special type of—

An n-bit binary counter can follow a counting sequence from—

The maximum number a counter can count is called its—

A counter having n flip-flops has a modulus of—

In a binary counter, the least significant bit (LSB) toggles—

Consider the following uses of counters: Which of the following is correct?

Digital devices refer to electronic devices capable of—

Which of the following is an example of a digital storage device?

A walkie talkie is an example of which type of digital device?

Large assemblies of logic gates packaged together for ease of use are known as—

Which of the following is at the core of creating components such as encoders, decoders and multiplexers?

Consider the following digital devices: Which of the following is correct?

What is the number of bits in Unicode?

How many different characters can be coded in Unicode?

What is the next value of the hexadecimal sequence 4, 8, C?

What is the 2's complement (8-bit representation) of the decimal number $-12$?

What is the equivalent hexadecimal number of $(1110.11)_2$?

If a gate has every input line as 0 and the output is 1, the gate is a— Which one is true?

$(110110)_2 = ?$ Which one is true?

What is 2's complement?

Why is Binary $1+1$ not the same as Boolean $1+1$?

উদ্দীপক: X, Y and Z bought books priced X = $(110110)_2$, Y = $(36)_8$ and Z = $(A9)_{16}$ taka. What is the price of Z in the decimal system?

উদ্দীপক: X, Y and Z bought books priced X = $(110110)_2$, Y = $(36)_8$ and Z = $(A9)_{16}$ taka. What is the price of X in the decimal system?

উদ্দীপক: X, Y and Z bought books priced X = $(110110)_2$, Y = $(36)_8$ and Z = $(A9)_{16}$ taka. What is the price of Y in the decimal system?

What is an adder?

Explain the theorem $M(M+M) = M$. Which Boolean property is applied? (Hint: $M+M=M$, then $M \cdot M = M$.)