Number system (Binary Number)
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This document explains binary number operations including addition, subtraction, multiplication, and division. It provides the rules and step-by-step workings for adding, subtracting, multiplying, and dividing binary numbers. Examples are shown of adding, subtracting, multiplying and dividing different binary numbers according to the rules provided.
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1) Binary addition and subtraction follow similar rules to decimal with 0+0=0, 0+1=1, 1+0=1, 1+1=10, and 1+1+1=11. To subtract larger binary numbers, subtract column by column.
2) 1's complement changes each 0 to 1 and vice versa, and is used to subtract by adding the 1's complement of the subtrahend to the minuend. 2's complement is 1's complement plus 1.
3) 2's complement subtraction discards any end around carry, while 1's and 2's complement allow binary subtraction. 9's and 10's complement work similarly to convert decimals.
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1) Binary addition and subtraction follow similar rules to decimal with 0+0=0, 0+1=1, 1+0=1, 1+1=10, and 1+1+1=11. To subtract larger binary numbers, subtract column by column.
2) 1's complement changes each 0 to 1 and vice versa, and is used to subtract by adding the 1's complement of the subtrahend to the minuend. 2's complement is 1's complement plus 1.
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2. It provides examples of addition in binary, decimal, and other number systems. Binary addition is demonstrated through examples of adding positive and negative numbers represented in 1's and 2's complement forms.
3. Additional examples show addition in decimal and other number bases such as octal and hexadecimal. Proper carrying and representation of results are emphasized.
Decimal arithematic operation
This document discusses decimal arithmetic operations using binary coded decimal (BCD) numbers. It describes how decimal numbers are represented in BCD format and processed using microoperations in the arithmetic logic unit (ALU). Addition and subtraction of decimal numbers are performed by converting the numbers to BCD, performing binary addition or subtraction on the digits, and converting the output back to decimal if needed. Block diagrams of BCD adders and examples of decimal addition and subtraction are provided.
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Number system (Binary Number)
- 2. BINARY ADDITION Rules : 0+0 = 0 0+1 = 1 1+0 = 1 1+1 = 0,1 in carry For Example : 101 +101 1010 Q2. 101 + 101 1011 +1011 10110 Q3. 1011 + 1011 • To add these two numbers, we first consider the "ones" column and calculate 1 + 1, which results in 10. We "carry" the 1 to the "tens" column, and the leave the 0 in the "ones" column. Q1. 100101 + 10101 100101 +10101 111010
- 3. Rules : 0 - 0 = 0 1 - 0 = 1 1 - 1 = 0 0 - 1 = 1 with a borrow of 1 Binary Subtraction Q1. 101 from 1001 1 0 0 1 -1 0 1 1 0 0 Q2. 111 from 1000 1 0 0 0 - 1 1 1 0 0 0 1 Q3. 1 1 0 0 1 0 1 0 from 1 0 0 1 1 0 1 1 1 1 0 0 1 0 1 0 - 1 0 0 1 1 0 1 1 0 0 1 0 1 1 1 1 Q4. 1010101.10 from 1111011.11 1 1 1 1 0 1 1 . 1 1 -1 0 1 0 1 0 1 . 1 0 0 1 0 0 1 1 0 . 0 1 11010.101 from 101100.011 1 0 1 1 0 0 . 0 1 1 - 1 1 0 1 0 . 1 0 1 1 0 0 0 1 . 1 1 0
- 4. Binary Multiplication Rules : 0 x 0 = 0 0 x 1 = 0 1 x 0 = 0 1 x 1 = 1 101 x11 101 101x 1111 11011 x101 11011 00000x 11011xx 1000111 Q1. 101 x 11 Q2. 11011 x 101
- 5. Q1. 11101.01 ÷ 1100 Solution: 1100) 11101.01 (10.0111 1100 10101 1100 0010 1100 1100 1100 Binary Division Rules : 0/0 = Zero Error 0/1 = 0 1/0 = Zero Error 1/1 = 1 Q2. 10110.1 ÷ 1101 Solution: 1101) 10110.1 (1.101 1101 10011 1101 11000 1101 1011