Convert each of the following hexadecimal representations to binary representation and then to i

Convert each of the following hexadecimal representations to...

Key Concepts

Numeral Systems

Numeral systems are methods to represent numbers using symbols and a base. Each numeral system, such as binary, decimal, and hexadecimal, uses a unique base to encode numeric values, with the position of each digit in a number representing a specific power of the base.

Hexadecimal Number System

The hexadecimal system is a base-16 numeral system that uses sixteen distinct symbols: 0-9 to represent values zero to nine, and A-F (or a-f) to represent values ten to fifteen. It is commonly used in computing because it can succinctly represent binary data.

Binary Number System

The binary system is a base-2 numeral system that uses two symbols, typically 0 and 1. It is the fundamental language of computers, where each digit represents a power of 2.

Decimal Number System

The decimal system is a base-10 numeral system that uses ten symbols, 0 through 9, and is the standard system for denoting integer and non-integer numbers in everyday use. Each digit's position represents a power of 10.

Base Conversion Techniques

Base conversion techniques involve transforming numbers from one numeral system to another, such as converting hexadecimal numbers to binary and then to decimal. This process utilizes the positional values associated with each base and the arithmetic operations needed to compute the number's equivalent in the target base.

Positional Notation

Positional notation is a method of representing or encoding numbers where the position of each digit in a number affects its value. Each digit is multiplied by the base raised to an exponent corresponding to its position, which is fundamental to performing conversions between numeral systems.

Transcript

00:01 So we have a couple hex things that we'd like to convert to binary and then to decimal.

00:08 Here's a, it's going to be relatively easy.

00:11 Zero cross a, so let's see, hexadecimal a corresponds to 1010, 1010 in binary, which is 2 plus 8, and that's going to be 10 in decimal, which is also what we see there.

00:28 That's relatively easy because it's one digit, but when we have two digits, as in part b, zero by one, cross one, four, converting to binary is relatively easy.

00:41 We just get 0001 for the one, and then 0100 for four, which is to say just 10100 if you'd like.

00:55 This is also going to be 16 plus 4 is 20 in decimal.

01:05 C, 1e, it will be again 0001, and then e corresponds to 1110, which is let's see, 124816, this is going to be 32 minus 2 is 30.

01:24 Yeah, 32 minus 2 because i said 1, 2, 4, 8, 16, this is the 16s bit, of course.

01:34 The next one would be 32, if this was all ones it would be 31, minus 1 again makes 30.

01:42 Next, so d, 28 is going to be 0010 for the two, and then 8 in hex is just 8 there, which is 2 times 16 is 32, plus 8 is 40.

02:00 I'm noticing a pattern here.

02:03 Let's see if that holds out.

02:05 E, 32, so that's going to be 11 for the three, and then 0010 for the two, which is also 3 times 16 is 48, plus 2 is 50.

02:19 F, 3c, 11, c is 1100, 1100.

02:29 That'll be 3 times 16 plus 12, 48 plus 12, wouldn't you know it is 60.

02:39 These do appear to be multiples of 10, but we don't get to assume that for free, they might try and throw a tricksy one.

02:48 G, let's see, so 4, 6, 4 is 10, 6 is 0110, and that'll be 64 plus 6 is indeed 70.

03:02 4 times 16 is 64.

03:05 H, 6, 5 is 0110, and then 0101, which is 6 times 16 is 96, i believe.

03:18 Let's just check that real quickly.

03:21 36, yep, 96.

03:24 Then 96 plus 5, see they're tricking here...

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