2 s complement

YES-NUMBER TOO LARGE FOR APU FORMAT NO-CNVRT TO 2 S COMPLEMENT STORE CNVRTD EXPONENT-NO CONV FOR NEG EXP GET HL, BC, DE ... 

For an integer type, the maximum size is 32 bits and the number is assumed to be in 2 s complement form. Optionally a synthesis system may perform data flow analysis of the model to determine the maximum size of an integer variable. For example,... 

Note that the adder logic with signed operands is the same as that with unsigned operands since the signed values are represented in 2 s complement form. 

Both word-level and bit-level parallelism should be exploited to reach the extreme throughputs which are needed in particular applications like radar processing [33]. Extensions in this direction are introduced in chapter 5. Employing the features of various arithmetic systems, such as 2 s complement and residue number systems (RNS) [42], bit-level systolic arrays can now be derived automatically. 

This will handle ihe operands as 2 s complemented values and return an appropriate signed array. The rules governing this arithmetic are discussed in Box 6.2. Overloading and function declarations are discussed later in this chapter. 

The package contains two functions called RIPPLE, both of which implement ripple-carry arithmetic. The reason for the two functions having the same name is discussed shortly. The first function adds two 2 s complemented signed numbers and returns not only the result but also an overflow bit. As a function can only return one value, the overflow must be concatenated with the result. Hence, the addition of two 4-bit numbers... 

Ripple carry addition/subtraction retums 2 s -complemented result no overflow... 

RIPPLE3 is a simpler architecture, although the function it calls is more flexible than the function called in RIPPLE I, for example. In this latest architecture, the ripple-cany function can add or subtract the 2 s complemented binary numbers. However, in this case it is called with a constant, (V. This means that the function will only ever be used for addition and so only the required elements of the function need to be s)mthesi2ed. The statistics in Table 6.2 show that the circuit produced is almost as small as the integer adder circuit. 

The arithmetic functions use a 2 s complement 16-bit fixed point representation. The precision of the arithmetic units is particularly crudal. Preliminary experiments with non-trivial problems such as character recognition imderlined the need to use 14 bits to specify the fraction portion of die number when using the most widely applied network, back-propagation on multilayer perceptrons. Most other models are satisfied with 8 bits. To accommodate these differences, the TNP PE offers a choice of two radices 8 bit and 14 bit. For a 16-bit word radix 8 allows a number range of approximately -128.00 to +127.99 (up to two decimal places precision), whereas radix 14 allows a range of around -2.0000 to +1.9999 (four ded-... 

The 16-bit 2 s complement adder design is contained in Figure 8.12. This is an extension of the ripple-carry adders designed in Chapter 6. A ripple-carry adder has been used rather than a cany-lookahead adder and so speed has been traded for area. The adder provides addition, subtraction and comparison operations. 

A boolean variable represents one or more signals. Each bit of a Boolean variable corresponds to a signal that can have value 0 or 1. The total number of bits is the size of the variable. If the size is one, then it is a scalar, otherwise, it is a vector. An integer value is rqiresented bit-wise using 2 s complement convention therefore, the acceptable values for a vector of size n range firom —2"/. .. (2 / — 1). The indices of a vector start from 0 to n — 1, where index 0 represents the least significant bit (LSB), and index n — 1 represents the most significant bit (MSB). 

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