Topic-6 ( Numbers and Logic )

What is base-8 called?

Octal

What is base-10 called?

Decimal

What is base-2 called?

Binary

What is base-16 called?

Hexadecimal

Octal digits range from?

0 to 7

Binary digits range from?

0 to 1

Hexadecimal digits range from?

0-9, then A=10, B=11, C=12, D=13, E=14, F=15

Convert octal 125 to decimal?

(1×64)+(2×8)+(5×1)=85

Binary digit weightings (5-bit example)?

16, 8, 4, 2, 1

Convert binary 10110 to decimal?

(1×16)+(0×8)+(1×4)+(1×2)+(0×1)=22

What is the "guessing" method for decimal→binary?

Visualise binary digit weightings

What is the "repeated division by 2" method?

Divide decimal by 2 repeatedly, collect remainders backwards

Convert 50 to binary using repeated division?

50 → remainder 0, 25→1, 12→0, 6→0, 3→1, 1→1 → 110010

Binary 110010 equals what decimal?

32+16+0+0+2+0=50

Add binary 0110111 + 010010

27 + 18 = 45 → 101101

Subtract binary 0110111 − 000110

27 − 6 = 21 → 010101

Multiply binary 0110111 × 101

27 × 5 = 135 → 10000111

How do computers perform subtraction?

Negate the 2's complement of the second number and add

What is 2's complement negation method?

Complement all bits (0→1,1→0), then add 1

What is 2's complement?

Negative binary representation where high order bit has negative positional value

In 8-bit 2's complement, what is the high order bit value?

-128

Convert 01110101 (2's complement) to decimal?

64+32+16+4+1 = 117

Convert 11110101 (2's complement) to decimal?

-128+64+32+16+4+1 = -11

8-bit 2's complement range?

-128 to +127

Complement of 10110100?

01001011

Negate 10110100 using 2's complement?

01001011 + 1 = 01001100 (76)

Negate 00100000 using 2's complement?

11011111 + 1 = 11100000 (-32)

How many bits per octal digit?

3 bits

How many bits per hexadecimal digit?

4 bits

Convert hex 0A to decimal?

10

Convert hex 0F to decimal?

15

Hexadecimal digits: what is A, B, C, D, E, F?

A=10, B=11, C=12, D=13, E=14, F=15

Convert hex 2F to decimal?

2×16 + 15 = 47

What is BCD?

Binary Coded Decimal — each decimal digit converted to 4-bit binary

How many bits per BCD digit?

4 bits (nibble)

Convert 57 to BCD?

0101 0111

Convert 57 to binary?

0011 1001

Convert 57 to hex?

39

What happens when BCD addition exceeds 9?

Add 6 (0110) to correct for the 6 disallowed codes (10-15)

Add 8+7 in BCD?

1000 + 0111 = 1111 → +0110 = 0001 0101 (BCD 15)

What is ASCII?

American Standard Code for Information Interchange — maps characters to numbers

How many bits in standard ASCII?

7 bits → 127 characters

What is extended ASCII?

Adds another 127 characters (total 256)

What is ASCII code for '0'?

48 decimal, 30 hex

What is ASCII code for 'A'?

65 decimal, 41 hex

What is ASCII code for 'a'?

97 decimal, 61 hex

What is Unicode?

16-bit character set → supports multiple languages, scripts, math symbols

ASCII vs Unicode main difference?

ASCII = 7-bit (English only), Unicode = 16-bit (multiple languages)

In computer logic, what numbers represent True and False?

True = 1, False = 0

AND truth table: 0 AND 0?

0

AND truth table: 0 AND 1?

0

AND truth table: 1 AND 0?

0

AND truth table: 1 AND 1?

1

OR truth table: 0 OR 0?

0

OR truth table: 0 OR 1?

1

OR truth table: 1 OR 0?

1

OR truth table: 1 OR 1?

1

NOT truth table: NOT 0?

1

NOT truth table: NOT 1?

0

Binary AND example: 10110100 AND 11001110?

10000100

Binary OR example: 10110100 OR 11001110?

11111110

Binary NOT example: NOT 10110100?

01001011

AND logic real-world example?

Both valves must be open for water to flow

OR logic real-world example?

Either valve open → water flows

NOT logic real-world example?

Light sensor — light on → glow off; light off → glow on