Lesson 3-Introduction to number system.pptx

TACLOBAN  ORMOC  MANDAUE On this session you are expected to: To introduce the number system To familiarize the conversion of number system. To determine the steps on how to convert number system to different bases. INTRODUCTION TO NUMBER SYSTEM What is a number system? is...

TACLOBAN  ORMOC  MANDAUE On this session you are expected to: To introduce the number system To familiarize the conversion of number system. To determine the steps on how to convert number system to different bases. INTRODUCTION TO NUMBER SYSTEM What is a number system? is a set of number, that can perform one or more arithmetic operation (MDAS) such as: – MULTIPLICATION – DIVISION – ADDITION – SUBTRACTION  BIT – Is a binary digit (0 & 1). BYTE – Is a series of eight bits (Binary digits) that are strung together. (01100111) There are 4 types of number system: 1.Binary (2) 2.Octal (8) 3.Decimal (10) 4.Hexadecimal (16)  BINARY is the fundamental number system of computer based system. It represents numeric values using two symbols, 0 and 1. – Example: 1011011 0011100  OCTAL Is a number system which has its base as “eight”. It uses numbers from 0 to 7 – “0”, “1”, “2”, “3”, “4”, “5”, “6”, “7”. Example: –  DECIMAL Is a number system which uses digits from 0 to 9 to represent a number with base 10. – “0”, “1”, “2”, “3”, “4”, “5”, “6”, “7”, “8”, “9”. Example: – –  HEXADECIMAL is a positional numeral system that represents numbers using a radix (base) of 16. It uses a combination of numbers from 0 – 9 and A-F to represent (10-15). Example: – CONVERSION OF NUMBER SYSTEM CONVERSION OF NUMBER SYSTEM CONVERSION OF NUMBER SYSTEM REPRESENTATION OF A BINARY NUMBER CONVERSION OF BINARY TO OTHER NUMBER SYSTEM  Convert Binary to Decimal Plot the given number in a table following the value of the number system as shown below. Add all the values from right to left at the position represented by 1’s. Then add the base of 10 in the final answer  Convert Binary to Decimal CONVERT:1010011 to decimal Step 1: Plot the given number in the table  Convert Binary to Decimal Step 2: Add all decimal digit value where the binary digit value is 1 Decimal digits with binary 1: - 64 + 16 + 2 + 1 = 83 Step 3: add the base 10 in the final answer - Therefore: Another way to convert Convert Binary to Octal 1. Group the given binary value into three starting from the right. NOTE: you have to pad/separate the digits to three in order to meet the requirement of 3 digit per group. 2. Add 4,2 and 1 underneath each binary number per group. Add find the sum of each group if it has more than 1 value that is represented by 1’s. Then concatenate all the values of each group then put the base of octal. Convert Binary to Octal CONVERT: 1010011 to OCTAL Step1: - 1|010|011 NOTE: that we must have 3 digits per pad/group therefore the grouped value is: - 0 0 1 | 0 1 0 | 0 1 1 – The zero’s in blue text are the added value Convert Binary to Octal Step 2: Add 4, 2 and 1underneath the binary value. BINARY VALUE - 001|010|011 OCTAL EXPONENTIAL VALUE - 4 2 1 421 421 Convert Binary to Octal Step 3: Add all octal where the number system is 1’s. Note all text in red in step 2 are the octal value with 1’s BINARY VALUE - 0 0 1 | 0 1 0 | 0 1 1 421 421 421 OCTAL EXPONENTIAL VALUE - ‘1’ + ‘2’ + ‘3’ = 123 Therefore,  Convert Binary to 1. Hexadecimal Group the given binary value into four starting from the right. NOTE: - that you have to pad/group the digits into four, in order to meet the requirement of 4 per group. 2. Add 8,4,2 and 1 underneath each binary number per group. 3. Add the hexadecimal value of a number system represented by 1’s  Convert Binary to Hexadecimal CONVERT: 1010011 to hexadecimal Step 1: Group the given binary value into four starting from the right –101|0011 NOTE: that we must have 4 digits per pad/group therefore the grouped value is: – 0 1 0 1 | 0 0 1 1 – The zero in blue text is the added value.  Convert Binary to Hexadecimal Step 2: – Add 8,4,2 and 1 underneath the binary value. BINARY VALUE - 0 1 0 1 | 0 0 1 1 HEXA EXPONENTIAL VALUE - 8 4 2 1 | 8 4 2 1  Convert Binary to Hexadecimal Step 3: Add all hexadecimal value where the number system is 1’s. Note all text in red in step 2 are the hexadecimal value with 1’s BINARY VALUE - 0 1 0 1 | 0 0 1 1 HEXA EXPONENTIAL VALUE - 8 4 2 1 | 8 4 2 1 5 + 3 = 53 Therefore, MIDTERM QUIZ 1: Given: 1111001. 1. Convert the Given number to Decimal. 2. Convert the Given number to Octal. 3. Convert the Given number to Hexadecimal. CONVERSION OF DECIMAL TO OTHER NUMBER SYSTEM  Convert Decimal to Binary 1. Write the decimal number as the dividend. Then add a slash (/) and write the base of the number system (in our case, "2" for binary) as the divisor outside the curve of the division symbol. 2. Divide the decimal number to the binary and write “0” if there is no remainder and 1 if there is. Continue to divide until you reach the quotient of “0”. Convert Decimal to Binary 3. Read the remainder/bit value upward from bottom to top. NOTE: In converting decimal to binary every remainder that is greater than 0 is considered as 1. Since binary only accepts two values which are 0 and 1.  Convert Decimal to Binary CONVERT: to Binary Step 1 & 2: Write the decimal number as the dividend in a division symbol and write the base of the destination system which is base 2. PLEASE REFER TO THE ILLUSTRATION >>>>>>>>>>>>>>>>>> Convert Decimal to Binary Convert Decimal to Binary Step 3: Read the remainder/bit value upward from bottom to top.  Convert Decimal to Octal 1. Divide the given decimal value to 8 until we reach 0 value. To get the remainder multiply the quotient by 8, then minus the given number. The result from the subtraction is the remainder. 2. Read the remainder/bit values upward to have the answer.  Convert Decimal to Octal CONVERT: to Octal Step 1: Divide the decimal value to the value of 8 as the radix/base of the octal. PLEASE REFER TO THE ILLUSTRATION >>>>>>>>>>>>>>>>>> Convert Decimal to Octal  Convert Decimal to Octal Step 2: Read the values Upward. PLEASE REFER TO THE ILLUSTRATION >>>>>>>>>>>>>>>>>>  Convert Decimal to Hexadecimal 1.Divide the given decimal value to 16 until we reach 0 value. To get the remainder multiple the quotient by 16 minus the given number. The result from the subtraction is the remainder. 2. Read the remainder/bit values upward.  Convert Decimal to Hexadecimal CONVERT: to Hexadecimal Step 1: Divide the decimal value to the value of 16 as the radix/base of the Hexadecimal PLEASE REFER TO THE ILLUSTRATION >>>>>>>>>>>>>>>>>> Convert Decimal to Hexadecimal Written Recitation: Given: 369 base of 10. 1. Convert the Given number to Binary. 2. Convert the Given number to Octal. 3. Convert the Given number to Hexadecimal. CONVERSION OF NUMBER SYSTEM CONVERSION OF OCTAL TO OTHER NUMBER SYSTEM  Convert Octal to Binary 1.Get the binary values of the given octal per digit. Refer to the table above for the binary value. 2.Read the answer downward CONVERSION OF NUMBER SYSTEM  Convert Octal to Decimal 1.Get the given octal value and find the value of 8 to the nth power. Multiply the given number to base 8 nth power. CONVERSION OF NUMBER SYSTEM  Convert Octal to hexadecimal 1. Convert the octal number to binary 2. Read the binary number downward then group into 4. 3. Convert the binary number grouped by 4 to hexadecimal. Grouping should start from right to left. 4. Add all with positive values and or equal to 1 CONVERT OCTAL TO HEXADECIMAL CONVERSION OF HEXADECIMAL TO OTHER NUMBER SYSTEM CONVERT HEXADECIMAL TO BINARY CONVERT HEXADECIMAL TO DECIMAL CONVERT HEXADECIMAL TO OCTAL