NUMBER SYSTEM AND CONVERSION

NUMBER SYSTEM AND CONVERSION. BASIC COMPUTING INTRODUCTION TO COMPUTING.

NUMBER SYSTEM AND CONVERSION. As we know, the number system is a form of expressing the numbers. In number system conversion , we will study on how to convert a number of one base, to a number of another base. There are a variety of number system such as binary numbers, decimal numbers, hexadecimal numbers, octal numbers, which can be exercised..

NUMBER SYSTEM CONVERSION TABLE. Binary Numbers Octal Numbers Decimal Numbers Hexadecimal Numbers 0000 0 0 0 0001 1 1 1 0010 2 2 2 0011 3 3 3 0100 4 4 4 0101 5 5 5 0110 6 6 6 0111 7 7 7 1000 10 8 8 1001 11 9 9 1010 12 10 A 1011 13 11 B 1100 14 12 C 1101 15 13 D 1110 16 14 E 1111 17 15 F.

NUMBER SYSTEM CONVERSION METHODS. Number system conversions deal with the operations to change the base of the numbers. For example, to change a decimal number with base 10 to binary number with base 2. We can also perform the arithmetic operations like addition, subtraction, multiplication on the number system. Here, we will learn the methods to convert the number of one base to the number of another base starting with the decimal number system..

Operation Output Remainder 25 ÷ 2 12 1(MSB) 12 ÷ 2` 6 0 6 ÷ 2 3 0 3 ÷ 2 1 1 1 ÷ 2 0 1(LSB).

Decimal to Hexadecimal: Again in decimal to hex conversion , we have to divide the given decimal number by 16. Example 3: Convert 128 10 to hex. Solution: As per the method, we can create a table;.

OTHER BASE SYSTEM TO DECIMAL CONVERSION. Binary to Decimal: In this conversion, binary number to a decimal number, we use multiplication method, in such a way that, if a number with base n has to be converted into a number with base 10, then each digit of the given number is multiplied from MSB to LSB with reducing the power of the base. Let us understand this conversion with the help of an example. Example 1. Convert (1101) 2 into a decimal number. Solution: Given a binary number (1101) 2 . Now, multiplying each digit from MSB to LSB with reducing the power of the base number 2. 1 × 2 3 + 1 × 2 2 + 0 × 2 1 + 1 × 2 0 = 8 + 4 + 0 + 1 = 13 Therefore, (1101) 2 = (13) 10.

REFERENCES. https://byjus.com/maths/number-system-conversion/.

BASIC COMPUTING. MAGNITUDE SIGNED BIT.

MAGNITUDE SIGNED BIT. Signed Binary Numbers Signed Binary Numbers use the MSB as a sign bit to display a range of either positive numbers or negative numbers.

POSITIVE AND NEGATIVE SIGNED BINARY NUMBERS. Signed Binary Numbers - Electronics-Lab.com.

SIGNED BINARY NUMBERS EXAMPLE 1. -15 10 as a 6-bit number ⇒ 101111 2 +23 10 as a 6-bit number ⇒ 010111 2 -56 10 as a 8-bit number ⇒ 10111000 2 +85 10 as a 8-bit number ⇒ 01010101 2 -127 10 as a 8-bit number ⇒ 11111111 2.

ONE’S COMPLEMENT OF A SIGNED BINARY NUMBER. One’s Complement or 1’s Complement as it is also termed, is another method which we can use to represent negative binary numbers in a signed binary number system. In one’s complement, positive numbers (also known as non-complements) remain unchanged as before with the sign-magnitude numbers. N egative numbers however, are represented by taking the one’s complement (inversion, negation) of the unsigned positive number. Since positive numbers always start with a “0”, the complement will always start with a “1” to indicate a negative number..

1’s COMPLEMENT USING INVERTERS. 1's complement using inverters.

ADDITION AND SUBRACTION USING ONE’S COMPLEMENT. One of the main advantages of One’s Complement is in the addition and subtraction of two binary numbers. In mathematics, subtraction can be implemented in a variety of different ways as A – B , is the same as saying A + (-B) or -B + A etc. Therefore, the complication of subtracting two binary numbers can be performed by simply using addition..

SUBTRACTION OF TWO BINARY NUMBERS. An 8-bit digital system is required to subtract the following two numbers 115 and 27 from each other using one’s complement. So in decimal this would be: 115 – 27 = 88 . First we need to convert the two decimal numbers into binary and make sure that each number has the same number of bits by adding leading zero’s to produce an 8-bit number (byte). Therefore:.

TWO’S COMPLEMENT. Two’s Complement or 2’s Complement as it is also termed, is another method like the previous sign-magnitude and one’s complement form, which we can use to represent negative binary numbers in a signed binary number system. In two’s complement, the positive numbers are exactly the same as before for unsigned binary numbers. A negative number, however, is represented by a binary number, which when added to its corresponding positive equivalent results in zero. In two’s complement form, a negative number is the 2’s complement of its positive number with the subtraction of two numbers being A – B = A + ( 2’s complement of B ) using much the same process as before as basically, two’s complement is one’s complement + 1..

4 BIT SIGNED BINARY COMPARISON. Decimal Signed Magnitude Signed One’s Complement Signed Two’s Complement +7 0111 0111 0111 +6 0110 0110 0110 +5 0101 0101 0101 +4 0100 0100 0100 +3 0011 0011 0011 +2 0010 0010 0010 +1 0001 0001 0001 +0 0000 0000 0000 -0 1000 1111 – -1 1001 1110 1111 -2 1010 1101 1110 -3 1011 1100 1101 -4 1100 1011 1100 -5 1101 1010 1011 -6 1110 1001 1010 -7 1111 1000 1001.