Materi Kuliah 1 - Sistem Bilangan || Pengantar Ilmu Komputer

Summary

This lecture delves into number systems, focusing on the decimal and binary systems. It covers key concepts such as the structure of decimal and binary numbers, the conversion between the two, and the operations performed with binary numbers like addition, subtraction, multiplication, and division. The session provides step-by-step explanations and examples of converting decimal to binary and vice versa. Students are encouraged to practice with exercises and are expected to understand these fundamental concepts, which are crucial for fields like computing and digital systems.

Takeaways

• 😀 The topic of the lecture is number systems, focusing on understanding different types like decimal and binary.
• 😀 Students are expected to learn how to convert decimal numbers to binary and vice versa.
• 😀 A number system is a set of rules for representing numbers, with examples being decimal, binary, hexadecimal, and octal.
• 😀 The decimal system is the most commonly used by humans and is based on 10 digits (0-9).
• 😀 In the decimal system, numbers can either be integers or decimal fractions (with a comma).
• 😀 The binary system uses only two digits, 0 and 1, and is fundamental to computer science.
• 😀 The process of converting decimal to binary involves dividing the decimal number by 2 and recording remainders.
• 😀 Binary to decimal conversion is done by multiplying each binary digit by its corresponding power of 2 and summing them up.
• 😀 Binary operations such as addition, subtraction, and multiplication follow specific rules, such as carrying over in addition.
• 😀 Subtraction in binary often involves borrowing from adjacent bits when needed.
• 😀 In binary multiplication, 0 multiplied by any number gives 0, and 1 multiplied by any number gives that number.
• 😀 Binary division follows the same basic principles as decimal division, involving repeated subtraction and division.

Q & A

What is a number system?

A number system is a set of symbols and rules used to represent numerical values. Common number systems include decimal (base-10), binary (base-2), hexadecimal (base-16), and octal (base-8).

What are the two main number systems discussed in this lecture?

The two main number systems discussed in this lecture are the decimal (base-10) and binary (base-2) systems.

How is the decimal number system structured?

The decimal system is based on 10 symbols (0-9), and each digit represents a value that is a power of 10, depending on its position in the number.

Can you explain the conversion of a decimal number like 7698 into its expanded form?

To convert 7698 into its expanded form, we break it down by position: 7 × 10^3 (7000), 6 × 10^2 (600), 9 × 10^1 (90), and 8 × 10^0 (8). Adding these together gives 7698.

What is a fractional decimal number, and how is it represented?

A fractional decimal number includes a fractional part after the decimal point. Each digit is multiplied by powers of 10, with negative exponents for digits after the decimal point.

How does the binary system differ from the decimal system?

The binary system uses only two symbols: 0 and 1, unlike the decimal system, which uses ten symbols (0-9). Binary is a base-2 system, whereas decimal is a base-10 system.

How do you convert a binary number like 1001 to decimal?

To convert binary 1001 to decimal, multiply each digit by powers of 2, starting from the right. 1 × 2^3 (8), 0 × 2^2 (0), 0 × 2^1 (0), and 1 × 2^0 (1). Adding these gives 9.

What is the method to convert a decimal number like 26 into binary?

To convert decimal 26 into binary, divide 26 by 2 repeatedly, recording the remainders. The binary representation of 26 is obtained by reading the remainders in reverse order: 11010.

What is the result of adding 1 + 1 in binary, and why?

In binary, 1 + 1 equals 0, with a carry-over of 1. This is because binary only uses 0 and 1, and when both digits are 1, the result exceeds the value of 1, so the sum wraps around to 0 with a carry.

How do you subtract binary numbers like 10 - 1?

To subtract binary numbers like 10 - 1, you perform borrowing. Since 0 cannot subtract 1, you borrow from the next digit, turning 10 into 2 (in binary, 10 is 2 in decimal), and the result is 1.