# Chapter 7 - PowerPoint PPT Presentation

1 / 20

Chapter 7. Arithmetic Operations and Circuits. 1. 7-1 Binary Arithmetic. Addition When the sum exceeds 1, carry a 1 over to the next-more-significant column. 0 + 0 = 0 carry 0 0 + 1 = 1 carry 0 1 + 0 = 1 carry 0 1 + 1 = 0 carry 1. 5. Binary Arithmetic. Addition

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

Chapter 7

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

## Chapter 7

Arithmetic Operations and Circuits

1

### 7-1 Binary Arithmetic

• When the sum exceeds 1, carry a 1 over to the next-more-significant column.

• 0 + 0 = 0 carry 0

• 0 + 1 = 1 carry 0

• 1 + 0 = 1 carry 0

• 1 + 1 = 0 carry 1

5

### Binary Arithmetic

• General form A0 + B0 = 0 + Cout

• Summation symbol ()

• Carry-out (Cout)

6

### Binary Arithmetic

• Carry-out is added to the next-more-significant column as a carry-in.

7

### Binary Arithmetic

• Subtraction

• 0  0 = 0 borrow 0

• 0  1 = 1 borrow 1

• 1  0 = 1 borrow 0

• 1  1 = 0 borrow 0

• General form A0B0 = R0 + Bout

• Remainder is R0

• Borrow is Bout

8

9

### Binary Arithmetic

• Subtraction

• When A0 borrows from its left, A0 increases by 210.

10

### Binary Arithmetic

• Multiplication

• Multiply the 20 bit of the multiplier times the multiplicand.

• Multiply the 21 bit of the multiplier times the multiplicand. Shift the result one position to the left.

• Repeat step 2 for the 22 bit of the multiplier, and for all remaining bits.

• Take the sum of the partial products to get the final product.

11

### Binary Arithmetic

• Multiplication

• Very similar to multiplying decimal numbers.

12

### Binary Arithmetic

• Division

• The same as decimal division.

• This process is illustrated in Example 7-4.

13

Example 7-4

14

Example 7-4 (Continued)

14

### 7-2 Two’s-Complement Representation

• Both positive and negative numbers can be represented

• Binary subtraction is simplified

• Groups of eight

• Most significant bit (MSB) signifies positive or negative

15

### Two’s-Complement Representation

• Sign bit

• 0 for positive

• 1 for negative

• Range of positive numbers (8-bit)

• 0000 0000 to 0111 1111 (0 to 127)

• Maximum positive number: 2N-1-1

• Range of negative numbers (8-bit)

• 1111 1111 to 1000 0000 (-1 to -128)

• Minimum negative number: -2N-1

16

### Decimal-to-Two’s-Complement Conversion

• If a number is positive,

• the two’s complement number is the true binary equivalent of the decimal number.

• If a number is negative:

• Complement each bit (one’s complement)

• Add 1 to the one’s complement

• The sign bit will always end up a 1.

18

18

### Two’s-Complement-to-Decimal Conversion

• If the number is positive (sign bit = 0), convert directly

• If the number is negative:

• Complement the entire two’s-complement number

• Do the regular b-to-d conversion to get the decimal numeric value

• Result will be a negative number

19

### Discussion Point

• Convert the following numbers to two’s-complement form:

3510

-3510

• Convert the following two’s-complement number to decimal:

1101 1101

20

### 7-3 Two’s-Complement Arithmetic

• Subtraction

• Convert number to be subtracted to a negative two’s-complement number

• Carry out of the MSB is ignored

21

### Discussion Point

• Add the following numbers using two’s complement arithmetic:

19 + 27

18 – 7

21 – 13

59 – 96

22