The Computer Code

1. Machine Representation of Instructions

   Reference Letter Used and Bit Allocation
   

   S	M	G	F	K	N
   (1)	(1)	(3)	(3)	(2)	(10)

   S = Program break digit - this digit is only used when using the machine in a multi-level mode.

   M = The mode bit

   G and F (Group and Function) together form the function code and are sometimes referred to by the single letter F.

   K = The modifier,

   K = 0	No modifier
   K = 1	B-register
   K = 2	Accumulator
   K = 3	Sequence Control Register (S.C.R.)

   N = The address bits.

   For convenience, the instruction format of the 502 program sheet is arranged in a slightly different sequence, illustrated on the specimen. The G and F bits are grouped under the single heading F and are entered in the first column; and the K-digit and the store mode bit occupy the last two columns.

   Instruction Code

2.1

Group 1 - Accumulator Functions

When the mode bit, M, is zero the address bits are used as a direct operand, e.g. the order 13 24 means, write the integer 24 into the accumulator, i.e. (i) a' = 24, where a indicates the previous content of the accumulator and a' its new content.

e.g.	(ii)	10 24	- add 24 into the accumulator		a' = a + 24
	(iii)	11 24	- subtract 24 from the accumulator		a' = a - 24
	(iv)	12 24	- subtract accumulator from 24		a' = 24 - a'
	(v)	To clear the accumulator		write 13 0
	(vi)	To count up		write 10 1
	(vii)	To count down		write 11 1

When the mode bit is a one - represented by a colon in the program sheet - the N bits are used to specify an address in the main store. The contents of the address specified are used in these functions. Thus if we indicate the contents of a main store address by the symbol (N) the meaning of each function is as follows.

F	M	A	B	S	Comments
10	:	N			a' = a + (N)
11	:	N			a' = a - (N)
12	:	N			a' = (N) - a
13	:	N			a' = (N)

Thus if the main store address 65 holds +99 and the accumulator holds +2:

F	M	A	B	S	Comments
10	:	65			a' = a + 99 = 101
11	:	65			a' = a - 99 = -97
12	:	65			a' = 99 - a = 97
13	:	65			a' = 99

When F > 3 the effect is to write the result into the main store location specified by N. Thus if (N)' represents the new contents of main store location N:

F	M	A	B	S	Comments
14	:	N			(N)' = (N) + a
15	:	N			(N)' = a - (N)
16	:	N			(N)' = (N) - a
17	:	N			(N)' = a

Example A

(a) Method of straight addition in the accumulator

Suppose x = 10 and the program commences at location 50.

Address of Instruction	F	M	A	B	S	Comments
50	13	:	600			Write the first number to the accumulator
51	10	:	601			Add in the second number
52	10	:	602			Add in the third number
53	10	:	603			Add in the fourth number
54	10	:	604			Add in the fifth number
55	10	:	605			Add in the sixth number
56	10	:	606			Add in the seventh number
57	10	:	607			Add in the eighth number
58	10	:	608			Add in the ninth number
59	10	:	609			Add in the tenth number
60	17	:	599			Store total

2.2

The B-register and Group 0 Orders

Group 0 orders operate on the B-register; otherwise they are identical to the group 1 orders.

Using b to denote the original contents of the B-register and b' tp denote the new contents, then:

F	M	A	B	S	Comments
00		N			b' = b + N
01		N			b' = b - N
02		N			b' = N - b
03		N			b' = N

When M = 1:

F	M	A	B	S	Comments
00	:	N			b' = b + (N)
01	:	N			b' = b - (N)
02	:	N			b' = (N) - b
03	:	N			b' = (N)
04	:	N			(N)' = (N) + b
05	:	N			(N)' = b - (N)
06	:	N			(N)' = (N) - b
07	:	N			(N)' = b

Example B

2.3

Groups 2 and 3 Orders

When M=0 these instructions deal with operations on the contents of fast store locations.

These two groups bear the same resemblance to each other as groups 0 and 1 orders, i.e. group 2 deals with b-line operations and group 3 deals with accumulator operations. Representing the original contents of a fast store location by n and the new contents by n', then

F	M	A	B	S	Comments
20		N			b' = b + n
21		N			b' = b - n
22		N			b' = n - b
23		N			b' = n
24		N			n' = b + n
25		N			n' = b - n
26		N			n' = n - b
27		N			n' = b

F	M	A	B	S	Comments
30		N			a' = a + n
31		N			a' = a - n
32		N			a' = n - a
33		N			a' = n
34		N			a' = a + n
35		N			a' = a - n
36		N			a' = n - a
37		N			a' = a

Example C

or

F	M	A	B	S	Comments
23		123			b' = x
20		123			b' = 2x
21		124			b' = 2x - y
00		3			b' = 2x - y + 3
27		125			store b

When M=1, the instructions deal with the contents of a main store location specified by N, e.g. if M=1 and fast store address 64 contains +85 and main store address 85 contains +700 the instruction 33 : 64 will write 700 in the accumulator.

Thus using (n) to indicate the contents of the main store location specified by N.

F	M	A	B	S	Comments
20	:	N			b' = b + (n)
21	:	N			b' = b - (n)
22	:	N			b' = (n) - b
23	:	N			b' = (n)
24	:	N			(n)' = (n) + b
25	:	N			(n)' = b - (n)
26	:	N			(n)' = (n) - b
27	:	N			(n)' = b

F	M	A	B	S	Comments
30	:	N			a' = a + (n)
31	:	N			a' = a - (n)
32	:	N			a' = (n) - a
33	:	N			a' = (n)
34	:	N			(n)' = (n) + a
35	:	N			(n)' = a - (n)
36	:	N			(n)' = (n) - a
37	:	N			(n)' = a

2.4

Other Simple Instructions

Count up in store:

	54	N	means n' = n + 1
	54 :	N	means (N)' = (N) + 1

Count down in store:

	55	N	means n' = n - 1
	55 :	N	means (N)' = (N) - 1

2.5

The Sequence Control Register and Jump Instructions

This register holds the address of the next instruction to be obeyed; under sequential operating conditions (e.g. example A) this register will be incremented by one as each instruction is obeyed. Before operating on example A The sequence control register will be 50; as instruction 50 is being obeyed the sequence control register will change to 51 - this process continues unless the sequence control register is changed by an instruction, i.e. a Jump instruction.

(a)	50	N	means jump to N in the fast store, i.e. s' = N (f.s.)
	50 :	N	means jump to N in the main store, i.e. s' = N (m.s.)
(b)	51	N	means reduce s by N, i.e. s' = s - N (fast store)
	51 :	N	means reduce s by N in main store, i.e. s' = s - N (main store)

It should be noted that since the sequence control register is normally incremented by one as each instruction is being obeyed, the effect of this instruction is to jump back N-1 places from the instruction being obeyed.

A stop instruction could therefore be:

	51	1
or	51 :	1	depending on the store being used.

(a) Test Zero

	46 [:]	N	means if a=0 set s' = N in fast store
	46 :	N	means if a=0 set s'=N in main store
	if a ≠ 0, the sequence control register operates in the normal manner, i.e. s' = s + 1
	42 [:]	N	means if b=0 set s'=N in fast store
	42 :	N	means if b=0 set s'=N in main store

This allows us to do example A by another method - by using a count of ten and counting down until this is zero.

Example D

Addition of 10 numbers by using a count:

Address of Instruction	F	M	A	B	S	Comments
50	13		10			) Set count of 10 in location 59
51	17	:	59			)
52	13	:	600			) Form sum of ten numbers in 599
53	14	:	599			)
54	55	:	59			Count down in count location
55	13	:	59			) Test count location
56	46	:	56			) if zero STOP
57	54	:	52			Modify instruction 52
58	50	:	52			Jump back

There are two weaknesses in the above program:

(a)

If there is anything but zero in location 599 this would be added into the total. This difficulty can be overcome by writing zero into 599 before obeying instruction 50. If possible the neccesary instructions would be written into locations 48 and 49 and the program commenced at instruction 48. Where this is not possible the two instructions would be written elsewhere in the store followed by a jump to location 50 - this is part of the program being obeyed before the above.

(b)

If it is required to operate on this program more than once, instruction 52 would have been modified after the first time of use. It is therefore found desirable to store somewhere in the program another copy of this instruction. This can be selected and written into location 52 either before the commencement of the program or before the stop instruction.

The program can be corrected as follows:

Address of Instruction	F	M	A	B	S	Comments
46	13		0			) Clear location which holds total
47	17	:	599			)
48	13	:	60			) Set instruction 52
49	17	:	52			)

and it would be neccesary to write into instruction 60:

60

13

:

600

Example E

Or it could be modified as follows:

Address of Instruction	F	M	A	B	S	Comments
48	13		0			) Clear result location
49	17	:	599			)
50	13		10			) Set count = 10
51	17	:	63			)
52	13	:	600			) Form sum
53	14	:	599			)
54	55	:	63			Count down in count
55	13	:	63			) Test count = zero
56	46	:	59			)
57	54	:	52			) Otherwise modify instruction 52
58	50	:	52			)
59	13	:	62			) Replace instruction 52
60	17	:	52			)
61	50	:	61			) STOP
62	13	:	600			) Used to replace instruction 52
63						) Used for count location

Further Conditional Jumps

44	N	means if a=0 or a positive set s' = N in fast store
44 :	N	means if a=0 or a positive set s' = N in main store
45	N	means if a is negative set s' = N in fast store
45 :	N	means if a is negative set s' = N in main store
47	N	means if the overflow indicator is set s' = N in fast store
47 :	N	means if the overflow indicator is set s' = N in main store

The overflow indicator is set whenever an attempt is made to exceed the maximum capacity of the accumulator or a store location.

Thus if: 524287 + N
or: -524287 - N (where N > 1) is attempted the overflow indicator is set.

The overflow indicator is cleared when it is examined by a 47 order. No other order will clear overflow; once overflow is set it remains set until examined.

As the computer regards everything as a fraction this should be expressed as follows: x ± y = z. Overflow if set when 1 ≤ z < -1.

Jumps affecting the B-register

(a) Count up and test B not zero

	40	N	means b' = b + 1. If now b=0 then s'=s+1
				but if now b ≠ 0 then s'=N (fast store)
	40 :	N	means b' = b + 1. If now b=0 then s'=s+1
				but if now b ≠ 0 then s'=N (main store)

(b) Count down and test non-zero in B

	41	N	means b' = b - 1. If now b=0 then s'=s+1
				but if now b ≠ 0 then s'=N (fast store)
	41 :	N	means b' = b - 1. If now b=0 then s'=s+1
				but if now b ≠ 0 then s'=N (main store)

(c) Subroutine Jumps

	43	N	means jump to N in the fast store (s' = N)
	43 :	N	means jump to N in the main store (s' = N)

In addition to changing the contents of the sequence control register to N the previous contents of the sequence control register are store[d] in b.

Thus:

b' = s+1

When the subroutine jump is from a main store program in addition to s + 1 being stored in b the most significant bit of b is set to indicate that it is from a main store program.

Example G

The Auxiliary Register

It is therefore found useful to have a supplementary register into which these bits can be placed. This register is known as the auxiliary register and it is 20-its long. However the most significant bit of this register[s] is frequently ignored - so it can best be regarded as a 19-bit register. Since the computer regards all numbers as fractions the multiplication of two large fractions need not neccesarily affect the auxiliary register. Thus .25 x .5 = .125.

Accumulator	00100		00000		00000		00000
				X
Store specified	01000		00000		00000		00000
				=
Accumulator	00010		00000		00000		00000
R	00000		00000		00000		00000

Integers are regarded by the computer as fractions scaled down by 2 ^-19 :

3 x 2 ^-19 x 3 x 2 ^-19 = 9 x 2 ^-38

or:

Accumulator	00000		00000		00000		00011
				X
Store specified	00000		00000		00000		00011
				=
Accumulator	00000		00000		00000		00000
R	00000		00000		00000		01001

The order that affects a register in this manner is the 64 order, i.e. double length multiplication. Thus:

	64	N	means ar' = a x n
	64 :	N	means ar' = a x (N)

There is also a single-length multiplication order (65 order) - this could have been used for the first example above. This produces a rounded multiplication; the auxiliary register being cleared by the instruction. Thus:

	65	N	means a' = a x n and r' = 0
	65 :	N	means a' = a x (N) and r' = 0

Just as it is desirable to have a double length product from a multiplication operation, it is also found desirable to have a double length dividend for a division operation. There are two division orders.

(1) Division with remainder (66).

In this operation the quotient appears in R and the remainder in a. Thus:

	66	N	means r' = ar/n and a' = ar - ar'
	66 :	N	means r' = ar/(N) and a' = ar - (n)r'

If overflow occurs in this instruction both a and r are meaningless.

(2) Rounded Division (67)

	67	N	means a' = ar / n
	67 :	N	means a' = ar/(N)

(a) Transfers between store and auxiliary register.

	53	N	means r' = n
	53 :	N	means r'= (N)
	57	N	means n' = r
	57 :	N	means (N)' = r

(b) Shift functions. Arithmetic double-length shift (62).

In this function the N digits are used to specify the number of places to be shifted. (The most significant bit of R being regarded as non-existent). Thus 62 19 would move the auxiliary register into the accumulator.

The effect of this function is to multiply the double-length ar by 2 ^N . Thus 62 1 means double ar.

Right shifts: Halving operations are achieved by using this order and specifying -N in the N digits. (alternatively it is possible to specify 1024-N for right shifts). Thus 62 -19 or 62 1005 would move the accumulator into the auxiliary register.

This function is an arithmetic shift thus the correct sign is maintained unless overflow occurs.

e.g. 62 -4 would have the following effect

a =	1.1011 00111 00011 11000	r =	01111 10000 01111 11000
a'=	1.1111 10110 01110 00111	r'=	01000 11111 00000 11111

Other Functions

Single length arithmetic shift (61) has the same effect as a 62 order but it does not affect the auxiliary register.

Logical shift (60) is a single length shift of the contents of the accumulator, without sign regeneration. Zero's are inserted where digits are missing.

If the order illustrated previously had been 60 -4 the result would have been:

a'=	00001 10110 01110 00111

Collating Instructions

52	N	means a' = a & n
52 :	N	means a' = a & (N)
56	N	means n' = a & n
56 :	N	means (N)' = a & (N)

Square Root Function (63)

This order finds the square root of the sum of the accumulator and the store location specified by N. Thus:

63	N	means a' = (a + n) ½
63 :	N	means a' = (a + (N)) ½

Instruction Modification

B-register Modification

Thus if b = 10 and the instruction 13 : 500 /1 is used this will set the contents of the main store address 510 into the accumulator.

Example H

Using a modifier to sum the numbers of example A.

Address of Instruction	F	M	A	B	S	Comments
50	13		0			) Clear result location
51	17	:	599			)
52	03		10
53	13	:	599	/1
54	14	:	599
55	41	:	53
56	50	:	56

All types of instructions can be modified. Thus if b = 10 and fast store location 35 holds +84:

13	5 /1	means a' = 15
33	25 /1	means a' = contents of fast store location 35 = 84
33 :	25 /1	means a' = contents of main store location 84
62	3 /1	means ar' = ar x 2 13

etc.

Accumulator modification

When k = 2 (indicated by /2) the accumulator is used as a modifier in the same manner as above.

If instruction 53 above had been 13 : 599 /2 the effect on this occasion would be to write the contents of 599 into the accumulator, and since this is zero the only effect of the program above would be to count zero into 599.

Note that it is possible to use the previous contents of the accumulator to modify an accumulator instruction; this also applies to b-line [modificatio] modification. Thus 13 10 /2 and 10 10 will have the same effect.

Example I

The above program compares the contents of each loaction with the next, gradually moving the smallest to the beginning. It then takes the remaining 15 numbers and compares them, moving the smallest of these to the beginning, and then compares the remaining 14 numbers moving the smallest of them to the beginning. It continues in a similar manner until all the numbers are in their correct order.

It is possible t write negative numbers to the acuumulator or b-line directly.

i.e.	11 5 /2	will subtract a + 5 from a therefore a = -5
	01 5 /1	will subtract b + 5 from b therefore b = -5

Sequence Control Modification

The sequence control register can also be used as a modifier. i.e. when K = 3 (/3 in the order code), this takes the prese[n]t contents of the sequence control register and adds these to the address digits before obeying the instruction.

NOTE:

Indirect Addressing Facilities

The sequence control register can be used as a modifier when attempting to write a subroutine for placing anywhere in the store.

Example J

Example E could be changed to a general routine for any store location as below.

Address [of] Instruction	F	M	A	B	S	[Comments]
x+0	56	:	7	/3
+1	50	:	6	/3
+2	13		0			) Clear results location
+3	17	:	599			)
+4	13		10			) Set modifier
+5	17	:	10	/3		)
+6	13	:	8	/3		) Set instruction in x + 8
+7	17	:	1	/3		)
+8	13	:	600			) Form sum
+9	14	:	599			)
+10	55	:	5	/3		) Count down in modifier
+11	13	:	4	/3		)
+12	46	:	1	/3		If zero jump to end
+13	51	:	14			Jump back
+14	51	:	1			[STOP]
+15	13	:	600
+16			+0			Modifier

Note that entry to this program is made at instruction x + 2. This is because, when using the sequence control register as a modifier, only locations following the present location can be addressed by this method, And, since in this program it is neccesary to modify an instruction after having obeyed that instruction, it is neccesary to jump to a section of program which is deliberately set before the beginning of the program proper.

Example K

Example H would therefore be written:

Address [of] Instruction	F	M	A	B	S
x+0	13		0
+1	17	:	599
+2	03		0
+3	13	:	599	/1
+4	14	:	599
+5	41	:	1	/3
+6	51	:	1
+7	51	:	5

Size of Store

As was mentioned earlier the fast store is 1,024 words long and therefore every location from 0-1.023 can be addressed directly. This is not so in the case of the main store where there are 16.384 locations: every location > 1,023 must therefore be accessed indirectly.

(1) Use of b-line or Accumulator as Modifier

Provided that the b-line or the accumulator is not required to hold a modifier or count, the b-line or accumulator could be used to access otherwise inaccessible locations.

i.e. If b = 2048, then 13 : 74 /1 would write the contents of main store location 2122 into the accumulator.

Similarly, if a = 2048, then 03 : 74 /1[2] would write the contents of main store location 2122 into the b-register.

(2) Use of Sequence Control Register Modification

This is similar to the above; however, it has the added limitation that:

(a)	No address prior to the current address can be accessed by this method.
(b)	Only addresses within the next 1,024 words can be accessed with this method.

(3) Use of Group 2 and 3 Functions

This is limited unless it is found desirable to access the same location n times or to change the fast store address holding the main store address, i.e. 33 : N /1 will access the contents of the main store address specified by N + b. It will not access the contents of main store address n + b.

Peripheral Instructions Group 7

Back - Contents - Next
Page created by Bill Purvis, last update 22nd November 2003
Contact me at: mailto:bill 'at' beeb.net