Divider Circuit for Encoded PCM Samples

The present application is related to the following copending and concurrently filed applications:

Ser. No. 06/687,877, filed Dec. 31, 1984, now U.S. Pat. No. 4,698,771, entitled ADDER CIRCUIT FOR ENCODED PCM SAMPLES

Ser. No. 06/687,892, filed Dec. 31, 1984, now U.S. Pat. No. 4,716,538, entitled MULTIPLY/DIVIDE CIRCUIT FOR ENCODED PCM SAMPLES

Ser. No. 06/687,875, filed Dec. 31, 1984, now U.S. Pat. No. 4,716,539, entitled MULTIPLIER CIRCUIT FOR ENCODED PCM SAMPLES

All of these inventions were invented by the same inventors and assigned to the same assignee.

The present invention relates to PCM signal processing circuitry and more particularly to a circuit for dividing D2 encoded PCM samples.

Prior art techniques for dividing D2 encoded PCM samples require conversion of the eight bit D2 encoded PCM sample into a thirteen bit linear coded sample. These samples are then divided and the resultant value is then reconverted to an eight bit D2 encoded number.

The present invention discloses a novel arrangement for performing division operations directly on the D2 encoded PCM samples without the requirement of first converting them to linear code and then reconverting the results of the numerical operation back to D2 code. Under the present invention, the D2 encoded PCM samples are interpreted to be in the form of floating point numbers. After the numerical operations have been performed the resultant number is normalized to account for an implied magnitude bit. Division is performed through multiplication with the reciprocal of the divider, which is found from a table in read-only-memory (ROM).

In accordance with the present invention a divider circuit is provided for use in a digital signal processing system which includes a source of pulse code modulation (PCM) samples and a source of divider numbers, each sample and number having a sign bit, a plurality of exponent bits and a plurality of mantissa bits. The divider circuit comprises a read-only-memory (ROM) connected to the source of divider numbers and operated in response to each of those numbers to provide the reciprocal of the mantissa and the negative of the exponent. An adder circuit and a multiplier circuit are both connected to the source of PCM samples and the ROM.

The adder circuit is operated to add the negative of the exponent bits to the PCM sample exponent bits and the multiplier circuit is operated to multiply the reciprocal mantissa bits by the PCM sample mantissa bits in order to effectuate division of said PCM sample.

FIG. 1 of the accompanying drawing is a combined block and logic diagram of the exponent adder circuit of the present invention;

FIG. 2 of the accompanying drawing is a combined block and logic diagram of the mantissa multiplier circuit of the present invention;

FIG. 3 of the accompanying drawing is a block diagram of the divider selection circuit of the present invention; and

FIG. 4 of the accompanying drawing is a logic diagram of the sign generator circuit of the present invention.

The circuit disclosed in the present invention operates directly on the D2 formatted samples without the need for conversion to linear code and reconversion to D2 code. In the D2 formatted "mu" law compressed code, bit positions have the following significance:

The three segment bits are used to indicate which of the eight possible segments contains the "mu" law encoded sample. The four magnitude bits are used to indicate one of the sixteen equally spaced locations within a particular segment. Magnitude bits M4-M1 are assigned weights of 2.sup.-1 -2.sup.-4. A fifth magnitude bit having the weight of 2.sup.0) is always implied and therefore it is not included in the D2 code. For example, the number 11011010 is negative (1 in the sign bit position) and is located in the fifth segment (101 in the segment bits) and in the tenth position (1010 in the magnitude bits) of that segment.

However, this number may be equally well interpreted as being a binary floating point number having a negative value (1 in the sign bit position) an exponent represented by segment bits 101 and a mantissa represented by magnitude bits 1010. These mantissa bits are similarly weighted from 2.sup.-1 to 2.sup.-4. With this arrangement the floating point number has a value of K.times.2.sup.-5 .times.(1+1/2+1/8) volts, where the mantissa value of 1 is defined as an implied bit, the mantissa value of 1/2 is represented by the first bit of the mantissa (first nonzero bit) as weighted by 2.sup.-1 and the mantissa value of 1/8 is equal to the third bit of the mantissa (second nonzero bit) as weighted by 2.sup.-3. The K factor determines the maximum value of the sample but it has no effect on the numerical floating point operations since all numbers have equal K factors in this application. Typically, K=1.

Each of the D2 encoded samples that is operated on by the present invention is referred to as Word #1. This word represents the multiplicand or dividend. The bits of Word #1 are referenced to S18, sign bit, E17, E16, and E15, exponent bits, and M14, M13, M12 and M11, mantissa bits.

The divider word operating on the D2 formatted number is referred to as Word #2. In this application the bits of Word #2 are referenced as S28, sign bit, E27, signed exponent bit, E26 and E25, exponent bits, and M24, M23, M22 and M21 mantissa bits. The exponent sign bit is required since the divider in practical application covers a range of numbers from fractional to larger than 1. In the case of fractional exponents, the exponents are actually negative whole numbers since the mantissa (with the implied bit) is always larger than 1.

Similarly, the output word provided by the present invention is referred to as Word #3 and has corresponding bit notations of S38, sign bit, E37, E36 and E35, exponent bits, and M34, M33, M32 and M31, mantissa bits. This word represents the product or quotient.

When dividing a D2 encoded sample, rules similar to those of floating point division are applied. Therefore, the exponents are subtracted and the difference of the exponents is then selected for the output exponents E35-E37.

The mantissa's, M11-M15 and the reciprocal of M21-M25, are subsequently multiplied. The resultant mantissa, M31A-M35A must be greater than or equal to 1 and less than 2 when normalized. Therefore, if the resultant mantissa, M31A-M35A, is greater than or equal to 2, a carry bit is generated. This bit is added to the exponent, E35-E37, and therefore the resultant mantissa, M31A-M35A, is shifted down by 1 bit position. If the exponent, E35-E37, then overflows, the maximum number (all ones in all bit positions except the sign bit) is generated.

In the case of division instead of multiplying with the reciprocal of the divisor, the exponents must be subtracted and the mantissas divided. In this case the resulting mantissa can become <1. Therefore, it would have to be renormalized (1 place left shift) and 1 would have to be subtracted from the exponent. If the resulting exponent value then would underflow, the minimum number must be substituted. However, division through multiplication with the reciprocal of the divider, as in the present invention, requires less circuitry since multiplication is easier to implement and is faster than the dividing process.

Referring now to FIG. 1 the exponent subtractor circuit of the present invention is shown. This circuit includes adder 100 which has a carry (C1) input, A1-A3 inputs, B1-B3 inputs, SUM1-SUM3 outputs and a carry (CRY) output. The C1 input is connected to the mantissa multiplier circuit of FIG. 2 via the mantissa overflow (MOVF) lead. The A1-A3 inputs are connected to the D2 data bus via E15-E17 leads and the B1-B3 inputs are connected to the divider selection circuit of FIG. 3. The SUM1-SUM3 outputs are connected to the first input of OR gates 110-112, respectively. The outputs of OR gates 110-112 are then connected to the first input of AND gates 120-122, respectively. The CRY output is connected to inverter 130 and the second input of AND gate 141 via the exponent overflow (EOVF) lead. The B3 input is further connected to inverter 140 and the second input of NAND gate 131 via the E27 lead. Inverter 130 is connected to the first input of NAND gate 131 via the EOVF lead and inverter 140 is connected to the first input of AND gate 141 via the E27 lead. AND gate 141 is connected to the second input of OR gates 110-112 via the SUBMAX lead. NAND gate 131 is connected to the second input of AND gates 120-122 via the SUBMIN lead. NAND gate 131 and AND gate 141 are further connected to the mantissa multiplier of FIG. 2 via the SUBMIN and SUBMAX leads, respectively, and AND gates 120-122 are connected to the D2 data bus via the E35-E37 leads, respectively. The exponent subtractor circuit performs exponent subtraction through two's-complement addition.

Since the three bit divisor exponent is in two's-complement notation the most significant bit (E27) represents the exponent sign bit and it also has a weight of -2.sup.2 =-4. The E26 and E25 bits have weights of 2.sup.1 =2 and 2.sup.0 =1, respectively. Thus, the notation 110 represents an exponent having a value of -4+2+0=-2. Similarly, the notation 010 represents an exponent having a value of -0+2+0=+2. Thus the exponent has a range of values of 100=-4 to 011=+3. The mantissa has an implied bit located to the left of the binary point and four fractional bits. Thus the mantissa covers a range of values of 1.0000=1 to 1.1111=1+1/2+1/4+1/8+1/16=1 15/16 The floating point divider can be written in the form of an exponent located to the left of a binary point and the fractional mantissa bits to the right of the binary point since the implied mantissa bit need not be indicated. Thus the floating point divider has a range from a minimum of 100.0000=2.sup.-4 =1/16 to a maximum of 011.1111=2.sup.3 .times.(1-15/16)=8.times.(31/16)=15 1/2.

The three bit exponent of Word #1 (E17-E15) is added to the reciprocal of the three bit exponent of Word #2 E27-E25) by adder 100. The D2 format for pulse code modulation (PCM) Word #1 has the following weights assigned to to its exponent bits: E17=-4, E16=-2 and E15=-1. Therefore, if exponent bits E17-E15 have values of 010 then the exponent has a value of -4+0-1=-5. Similarly, if the exponent bits have values of 000 then the exponent has a total value of -4-3-1=-7 and if the exponent bits have values of 111 then the exponent has a total value of -0-0-0=0. Thus, the exponent of Word #1 is represented in one's-complement notation.

This notation is used because the maximum value of the analog voltage of the PCM sample equals approximately 2. Therefore, in normalized form without showing the implied mantissa bit, the maximum analog voltage can be represented as 111.1111. The three exponent bits to the left of the binary point represent an exponent value of 0 and the four fractional mantissa bits have values of 1/2, 1/4, 1/8, and 1/16. Thus the exponent factor for the analog voltage can be represented as 2.sup.0 and the conventional normalized mantissa (implied bit shown) can be represented as 1+1/2+1/4+1/8+1/16=1 15/16. Therefore the maximum analog voltage is represented in floating point form as 2.sup.0 .times.(1 15/16=1 15/16 which is approximately 2.

The minimum value for the analog voltage can be represented as 000.0000 with a resultant exponent value of -7 and fractional mantissa bit values of 0, 0, 0, 0. Thus the analog voltage can be represented with the conventional normalized mantissa (implied bit shown) as 2.sup.-7 .times.1+0+0+0+0=2.sup.-7 .times.1=2.sup.-7 =1/128. Therefore the analog voltage has a range of 1/128 thru 1 15/16.

However, adder 100 adds Word #1 which has an exponent in one's-complement notation to the negative exponent of Word #2 which has an exponent in two's-complement notation. The result of the addition must produce an exponent in one's-complement notation for proper PCM coding in the D2 format. Rather than converting one of the words to the notation form of the other in order to perform addition in the same notational scheme, the present invention adds the two words directly by utilizing the following algorithm rules: (1) if adder 100 produces a sum exponent having a value greater than zero, i.e., binary 111, this sum is replaced with the maximum allowed exponent of binary 111; and (2) if adder 100 produces a sum exponent having a value less than -7, i.e., binary 000, this sum is replaced with the minimum allowed value of binary 000.

The logical operations performed by the exponent adder are derived from the following table:

Thus, the exponent adder circuit applies the following logical rules: (1) if the multiplier exponent is positive and a carry condition results from the exponent addition, substitute the maximum PCM value (111) for the quotient exponent; (2) if the multiplier exponent is negative and a carry condition does not result from the exponent addition, substitute the minimum PCM value (000) for the quotient exponent; and (3) in all other cases, use the results of the exponent addition for the quotient exponent.

Thus, the quotient exponent is provided in correct D2 format without conversion of the exponent of the multiplier (Word #2), multiplicand (PCM sample word, Word #1) or quotient to a different code. The logic equations for these maximum and minimum substitutions are as follows:

These equations are implemented by NAND gate 131 and AND gate 141.

The exponent bits of Word #1 are received from the D2 data bus and appear at the A1-A3 inputs of adder 100 in one's-complement format. The exponent bits for Word #2 are received from the ROM circuit and appear at the B1-B3 inputs of adder 100 in two's-complement format. Adder 100 adds the exponent bits of Word #1 to those of Word #2 and provides the sum therefore at outputs SUM1-SUM3.

The signals appearing at these outputs represent the exponent bits for the quotient exponent and are applied to the first input of OR gates 110-112. If AND gate 141 provides a logic level 0 signal on the SUBMAX lead then the signals provided at the SUM1-SUM3 outputs are gated by gates 110-112 to the first input of AND gates 120-122, respectively. Similarly, if NAND gate 131 applies a logic level 1 signal to the SUBMIN lead AND gates 120-122 gate the exponent bits from OR gates 110-112 to the D2 data bus via leads E35-37. Thus the exponent bits for the quotient appear on leads E35-E37.

However, if there is no exponent overflow condition as indicated by logic level 0 signal at the carry (CRY) output then a logic level 0 signal appears on the EOVF lead. Inverter 130 then applies logic level 1 signal to the EOVF lead. This logic level 1 signal than appears at the first input of NAND gate 131. If a logic level 1 signal also appears at the most significant exponent bit (E27), then that logic level 1 signal also appears at the second input of NAND gate 131. Consequently, a logic level 0 signal appears on the SUBMIN lead. This logic level 0 signal then appears at the second input of AND gates 120-122, causing them to provide logic level 0 signals on leads E35-E37. Thus the minimum value (000) for the exponent bits of the quotient word (Word #3) appear on leads E35-E37 when there is no exponent overflow and the most significant bit of the exponent of Word #2 is a 1.

Similarly if there is an overflow condition as indicated by logic level 1 signal at the CRY output then this logic level 1 signal appears on the EOVF lead and consequently at the second input of AND gate 141. If the most significant bit of the exponent of Word #2 (E27) is at logic level 0 then that signal is inverted to a logic level 1 by inverter 140 and applied to the first input of AND gate 141. Consequently AND gate 141 provides a logic level 1 signal to the SUBMAX lead and this logic level 1 signal appears at the second input of OR gates 110-112. These OR gates then apply logic level 1 signals to the first input of AND gate 120 which then gates them to leads E35-E37 since NAND gate 131 provides a logic level 1 signal under these conditions. Thus, the maximum value (111) for the exponent bits of the quotient word (Word #3) is provided when there is an exponent overflow and the most significant bit of the exponent of Word #2 (E27) is at a logic level 0.

If a mantissa overflow condition occurs when the mantissa of Word #1 and Word #2 are multiplied together then the logic level 1 signal also appears on the mantissa overflow (MOVF) lead. Consequently this logic level 1 signal would appear at the carry (C1) input of adder 100 and would be added together with the exponent bits of Word #1 and Word #2.

Referring now to FIG. 2 the mantissa multiplier circuit of the present invention is shown. Multiplier 200 includes inputs A2.sup.0 -A2.sup.3 which are connected to the D2 data bus via leads M11-M14, respectively. This multiplier also includes inputs B2.sup.0 -B2.sup.3 which are connected to the divider selection circuit via leads M21-M24, respectively. Inputs A2.sup.4 and B2.sup.4 are connected to the output of inverter 201 the input of which is connected to ground and thus a logic level 1 signal appears at these inputs. Multiplier 200 also includes outputs AB2.sup.0 -AB2.sup.9.

Data selector 210 includes inputs A1-A4, B1-B4 and select (SEL) B. The SEL B input is connected to the AB2.sup.9 output of multiplier 200 via the mantissa overflow (MOVF) lead which is also connected to the exponent subtractor circuit of FIG. 1. Output AB2.sup.8 of multiplier 200 is connected to input B1 of data selector 210; output AB2.sup.7 of multiplier 200 is connected to inputs A1 and B2 of data selector 210 and output AB2.sup.6 of multiplier 200 is connected to inputs A2 and B3 of data selector 210. Output AB2.sup.5 of multiplier 200 is connected to inputs A3 and B4 of data selector 210 and output AB2.sup.4 of multiplier 200 is connected to input A4 of data selector 210.

This data selector also includes outputs Y1-Y4 with respective weights which are connected to the first input of OR gates 220-223, respectively. These OR gates are connected to the first input of AND gates 230-233 which are connected to the D2 data bus via leads M34-M31, respectively. OR gates 220-223 have their second input connected to the exponent subtractor circuit of FIG. 1 via the SUBMAX lead while AND gates 230-233 have their spaced input connected to the exponent subtractor circuit of FIG. 1 via the SUBMIN lead.

Since the mantissa of words #1 and #2 are normalized, the logic level 1 signals for the implied bit positions must be entered into the multiplication process. Such logic level 1 implied bit values appear at the A2.sup.4 and B2.sup.4 inputs of multiplier 200. The fractional bit values for the mantissa of Word #1 then appears at inputs A2.sup.0 -A2.sup.3 via leads M11-M14, respectively, and the fractional bit values for the mantissa of Word #2 appear at the B2.sup.0 -B2.sup.3 inputs via leads M21-M24, respectively.

When two normalized numbers, 1+X1 and 1+X2, are multiplied together they produce a product of 1+X1+X2+X1X2. Both X1 and X2 are greater than or equal to 0 and less than or equal to 15/16ths. If X1+X2+X1X2 is less than 1, a carry condition will not occur at output AB2.sup.9 of multiplier 200. Consequently, there is no multiplication overflow and the product mantissa does not need to be shifted.

If X1+X2+X1X2 is greater than 1, for example when X1=X2=1/2, a carry condition does occur and a logic level 1 signal appears at the AB2.sup.9 output. This signal indicates that the multiplier circuit has overflowed and that the mantissa of the quotient is greater than 2. Thus the exponent for the quotient must be increased by 1 and the mantissa for the quotient must be divided by 2. Such division by 2 is accomplished by shifting the mantissa by one bit position to the right.

Therefore, the implied bit is shifted into the most significant bit of the quotient word and the most significant bit is shifted into the next most significant bit position, etc. This shifting operation is performed by data selector 210. When a logic level 1 signal appears on the multiplication overflow (MOVF) lead, this signal appears at the select (SEL) B input of data selector 210. Consequently, data selector 210 gates the signals appearing at its B1-B4 inputs to Y1-Y4 outputs, respectively. If a logic level 0 signal appears on the MOVF lead and therefore at the SEL B input, data selector 210 does not perform a shifting operation and consequently it gates the signals appearing at its A1-A4 inputs to Y1-Y4 outputs, respectively.

When a multiplication overflow condition results the quotient word is shifted left by one bit position. However, the exponent is also incremented by 1 since the logic level 1 signal appearing on the MOVF lead also appears at the carry (C1) input of the exponent subtractor circuit of FIG. 1.

Thus, multiplier 200 multiplies the normalized mantissa of Word #1 by the normalized mantissa of Word #2. The four most significant fractional bits of the quotient word then appear at bits AB2.sup.7 -AB2.sup.4 and implied bit appears at output AB2.sup.8. If there is an overflow condition, then the quotient word is greater than or equal to two and the overflow bit appears at the AB2.sup.9 output.

When no overflow occurs no shifting of the mantissa is required and consequently the implied bit is dropped since only fractional mantissa bits appearing at outputs AB2.sup.7 -AB2.sup.4 appear at inputs A1-A4 of data selector 210. Under this "no overflow" condition the signals appearing at inputs A1-A4 are gated directly to outputs Y1-Y4.

If there is an overflow condition the quotient mantissa is shifted down by one bit position and the implied bit is then shifted into the most significant fractional bit position. This implied bit appearing at the AB2.sup.8 output is connected to the B1 input of data selector 210. The three most significant fractional bits of the quotient word appearing at outputs AB2.sup.7 -AB2.sup.5 of multiplier 200 are connected to inputs B2-B4, respectively. Since under these conditions an overflow does occur the B inputs are selected and therefore gated to outputs Y1-Y4 of data selector 210.

When it is determined that minimum or maximum values must be provided in the mantissa bits of the output word, either a logic level 0 signal appears on the SUBMIN lead to force the mantissa bits to the minimum value or a logic level 1 signal appears on the SUBMAX lead to force the output word mantissa bits to the maximum value.

When it is intended to provide the maximum value for the mantissa bits the logic level 1 signal on the SUBMAX lead causes OR gates 220-223 to apply logic level 1 signals to the first input of AND gates 230-233. Since a logic level 1 signal appears on the SUBMIN lead under these conditions, AND gates 230-233 than apply logic level 1 signals to the D2 data bus via leads M34-M31, thereby indicating that the fractional mantissa bits of the Word #3 mantissa all have a value of one.

If it is determined that the output mantissa should have the minimum value, then a logic level 0 signal appears on the SUBMIN lead and consequently AND gates 230-233 apply logic level 0 signals to the D2 data bus via leads M34-M31, thereby indicating that the fractional mantissa bits of the output word have the minimum value of all zeros.

In the event that the mantissa bits of Word #3 do not need to be forced to the minimum or maximum values than a logic level 0 signal appears on the SUBMAX lead and a logic level 1 signal appears on the SUBMIN lead. Consequently, the output signals from data selector 210 are gated by OR gates 220-223 to AND gates 230-233 which then apply them directly to the D2 data bus via leads M34-M31.

Referring now to FIG. 3 the divider selection circuit of the present invention is shown. Read-only-memory 300 is connected to the divider data bus via leads E27A-E25A, and M24A-AM21A. This read-only-memory is also connected to a clock via the READ lead. Read-only-memory 300 also has outputs connected to leads E27-E25 and M24-M21.

Division is accomplished through multiplication with the reciprocal of the divisor. Thus the previously described multiplication operations apply equally to the division operation when the reciprocal of the divisor is used as the multiplier. Read-only-memory 300 is a 128 word by 8 bit memory. This memory contains 7 bit words that are the reciprocal of the 7 bit divider words.

The 7 divisor bits appearing on leads E27A-E25A and M24A-M21A are used as address bits for read-only-memory 300. Upon receipt of a periodic read signal from the clock circuit, read-only-memory 300 provides a 7 bit word which is the reciprocal of the address of that word. Thus, the signals appearing on leads E27-E25 and M24-M21 represent the exponent and mantissa bits, respectively, of the reciprocal of the divider signals appearing on leads E27A-E25A and M24A-M21A, respectively.

Referring now to FIG. 4 the sign generator circuit of the present invention is shown. Exclusive-OR gate 400 is used to determine the sign of the quotient. This exclusive-OR gate is connected to the D2 data bus via lead S18 and to the divider data bus via lead S28. The signal appearing on lead S18 represents the sign of the D2 PCM sample word (Word #1) and the signal appearing on the S28 lead represents the sign bit of the divider word (Word #2).

When dividing, if the sign bit of the two operands is identical, then the sign bit of the quotient is positive. However, if the sign bits of the two operands are different during a division operation, then the sign bit of the quotient is negative. Consequently, exclusive-OR gate 400 provides a logic level 0 signal, which represents a positive sign bit, when either logic level 0 or 1 signals appear on both the S18 and S28 leads. However, exclusive-OR gate 400 provides a logic level 1 signal (negative sign bit) on lead S38 when the signals appearing on the S18 and S28 leads are different. The sign bit for the quotient word (Word #3) is then applied by exclusive-OR gate 400 to the D2 data bus via lead S38.

Thus the divider circuit of the present invention utilizes an adder circuit to subtract the exponents of the dividend and divisor. These exponents are subtracted directly even though one of the operands is in two's-complement format and the other is in one's-complement format. In the event that the resultant subtraction of the exponents is greater than or smaller than predetermined maximum and values, additional circuitry ensures that the exponent of the quotient word does not exceed these predetermined minimum and maximum values. The present invention also includes a multiplier circuit which multiplies the mantissas of the two operands and limits the mantissa of the quotient word to predetermined minimum and maximum values. A read-only-memory is used to provide a reciprocal of the divider word, so that division can be accomplished through multiplication with such reciprocal, and an exclusive-OR gate is used to determine the sign bit for the resultant quotient word.

It will be obvious to those skilled in the art that numerous modifications of the present invention can be made without departing from the spirit of the invention which shall be limited only by the scope of the claims appended hereto.