The binary number system is the most natural system for a computer, but people are accustomed to the decimal system. One way to solve this conflict is to convert all input decimal numbers into binary numbers, let the computer perform all arithmetic operations in binary and then convert the binary...

## Floating-point representation

A floating-point number is said to be normalized if the most significant digit of the mantissa is nonzero. For example, the decimal number 350 is normalized but 00035 is not. Regardless of where the position of the radix point is assumed to be in the mantissa, the number is normalized only if its...

## Common Bus System

The basic computer has eight registers, a memory unit, and a control unit (to be presented in Sec. 5-4). Paths must be provided to transfer information from one register to another and between memory and registers.

## Register-Reference Instructions

Register-reference instructions are recognized by the control when 07 = 1 and I = 0. These instructions use bits 0 through 11 of the instruction code to specify one of 12 instructions. These 12 bits are available in IR(0-11). They were also transferred to AR during time T2•

## Input-Output and Interrupt

A computer can serve no useful purpose unless it communicates with the external environment. Instructions and data stored in memory must come from some input device. Computational results must be transmitted to the user through some output device. Commercial computers include many types of

## LDA: Load to AC

This instruction transfers the memory word specified by the effective address to AC. The rnicrooperations needed to execute this instruction are

## Shift Microoperations -circular shift

The circular shift (also known as a rotate operation) circulates the bits of the register around the two ends without loss of information. This is accomplished by connecting the serial output of the shift register to its serial input.

## Control of Registers and Memory

The registers of the computer connected to a common bus system are shown in Fig. 5-4. The control inputs of the registers are LD (load), INR (increment), and CLR (clear). Suppose that we want to derive the gate structure associated with the control inputs of AR. We scan Table 5-6 to find all the ...

## STA: Store AC & BUN: Branch Unconditionally

This instruction stores the content of AC into the memory word specified by the effective address. Since the output of AC is applied to the bus and the data input of memory is connected to the bus, we can execute this instruction with one microoperation:

## DATA TYPES

Binary information in digital computers is stored in memory or processor registers. Registers contain either data or control information. Control information Is a bit or a group of bits used to specify the sequence of command signals needed for manipulation of the data in other register

## Instruction Codes

In this chapter we introduce a basic computer and show how its operation can be puter specified with register is defined by its internal transfer registers, statements. the limirlg The otganization and control of structure, the comand the set of instructions that It uses. The design of...

## Control of Single Flip-flops

The control gates for the seven flip-flops can be determined in a similar manner. For example, Table 5-6 shows that lEN may change as a result of the two instructions ION and !OF.

## Integer Representation

When an integer binary number is positive, the sign is represented by 0 and the magnitude by a positive binary number. When the number is negative, the sign is represented by 1 but the rest of the number may be represented in one of three possible ways:

## Subtraction of Unsigned Numbers-2

Since we are dealing with unsigned numbers, there is really no way to get an unsigned result for the second example.

## OCTAL AND HEXADECIMAL NUMBER CONVERSION

The conversion from and to binary, octal, and hexadecimal representation plays an important part in digital computers. Since 23 = 8 and 24 = 16, each octal digit corresponds to three binary digits and each hexadecimal digit corresponds to four binary digits.

## operation code

An instruction code is a group of bits that instruct the computer to perform a specific operation. It is usually divided into parts, each having its own particular interpretation. The most basic part of an instruction code is its operation part. The operation code of an instruction is a group of ...

## Floating-Point Representation

The floating-point representation of a number has two parts. The first part represents a signed, fixed-point number called the mantissa. The second part designates the position of the decimal (or binary) point and is called the exponent. The fixed-point mantissa ...

## ARITHMETIC SUBTRACTION

Subtraction of two signed binary numbers when negative numbers are in 2' s complement form is very simple and can be stated as follows: Take the 2's complement of the subtrahend (including the sign bit) and add it to the minuend (including the sign bit). A carry out of the sign bit position is di...

## CONVERSION - INTRODUCTION

Conversion from decimal to its equivalent representation in the radix r system is carried out by separating the number into its integer and fraction parts and converting each part separately.

## Bus and Memory Transfers

A typical digital computer has many registers, and paths must be provided to transfer information from one register to another. The number of wires will be excessive if separate lines are used between each register and all other registers in the system.

## Control Logic Gates

he block diagram of the control logic gates is shown in Fig. 5-6. The inputs to this circuit come from the two decoders, the I flip-flop, and bits 0 through 11 of IR. The other inputs to the control logic are: AC bits 0 through 15 to check if AC = 0 and to detect the sign bit in AC(

## Timing and Control -2

The last three waveforms in Fig. 5-7 show how SC is cleared when D3T4 = I. Output D3 from the operation decoder becomes active at the end of timing signal T2• When timing signal T4 becomes active, the output of the AND gate that implements the control function D3T4 becomes active. This signal is ...

## ADD to AC

This instruction adds the content of the memory word specified by the effective address to the value of AC. The sum is transferred into AC and the output carry C,., is transferred to the E (extended accumulator) flip-flop. The rnicrooperations needed to execute this instruction are

## Input - output Register

The input register INPR consists of eight bits and holds an alphanumeric input information. The 1-bit input flag FGI is a control flip-flop. The flag bit is

## Instruction Cycle

A program residing in the memory unit of the computer consists of a sequence of instructions. The program is executed in the computer by going through a cycle for each instruction. Each instruction cycle in turn is subdivided into a sequence of subcycles or phases. In the basic computer each inst...

## Fixed-Point Representation

Positive integers, including zero, can be represented as unsigned numbers. However, to represent negative integers, we need a notation for negative values. In ordinary arithmetic, a negative number is indicated by a minus sign and a positive number by a plus sign.

## Hardware Implementation

The hardware implementation of logic rnicrooperations requires that logic gates be inserted for each bit or pair of bits in the registers to perform the required logic function. Although there are 16 logic rnicrooperations, most computers use only four-AND, OR, XOR (exclusive-OR), and complementf...

## Complements -2

The r's complement of an n-digit number N in base r is defined as r' - N for N * D and D for N = D. Comparing with the (r - I)'s complement, we note that the r's complement is obtained by adding I to the (r - I)'s complement since r' - N = [(r' - I) - N] + I.

## Binary Adder

To implement the add microoperation with hardware, we need the registers that hold the data and the digital component that performs the arithmetic addition. The digital circuit that forms the arithmetic sum of two bits and a previous carry is called a full-adder .

## Memory Transfer

The operation of a memory unit was described in Sec. 2-7. The transfer of information from a memory word to the outside environment is called a read operation.