**TI-84 Plus CE: Bitwise Operations**

**Introduction**

The programs NOT, AND, OR, and XOR are presented for the TI-84 Plus CE for integer in decimal base.

**NOT**

For integers x > 0, the NOT function is defined as:

Σ( 2^n * ( floor(x/2^n) mod 2 + 1 ) mod 2 ) from n = 0 to floor(log(x)/log(2))

However, observing the NOT operation on scientific calculators, the not function can be used for integers:

-(x + 1)

**TI-84 Plus CE Program NOT**

"2020-05-11 EWS"

Disp "NOT(X), X>0"

Prompt X

(X+1)→N

Disp "NOT X = ",N

Examples:

NOT 192: Returns -193

NOT -52: Returns 51

**AND**

For positive integers x, y and for x ≥ y, the AND function is defined as:

Σ( 2^n * ( [ floor(x/2^n) mod 2 ] * [ floor(y/2^n) mod 2 ] ) from n = 0 to floor(log(x)/log(2))

**TI-84 Plus CE Program AND**

"2020-05-11 EWS"

Disp "X AND Y, X≥Y"

Prompt X,Y

0→T

For(N,0,X-fPart(X))

(X/2^N)-fPart(X/2^N)→A

2*fPart(A/2)→A

(Y/2^N)-fPart(Y/2^N)→B

2*fPart(B/2)→B

T+2^N*A*B→T

End

Disp T

Examples:

145 AND 37: Returns 1

226 AND 125: Returns 96

**OR**

For positive integers x, y and for x ≥ y, the OR function is defined as:

Σ( 2^n *

[ [ ( floor(x/2^n) mod 2) + ( floor(y/2^n) mod 2 ) + ( floor(x/2^n) mod 2 * floor(y/2^n) mod 2) ] mod 2 ] from n = 0 to floor(log(x)/log(2))

**TI-84 Plus CE Program OR**

"2020-05-11 EWS"

Disp "X OR Y, X≥Y"

Prompt X,Y

0→T

For(N,0,X-fPart(X))

(X/2^N)-fPart(X/2^N)→A

2*fPart(A/2)→A

(Y/2^N)-fPart(Y/2^N)→B

2*fPart(B/2)→B

T+2^N*2*fPart((A+B+A*B)/2)→T

End

Disp T

Examples:

145 OR 37: Returns 181

226 OR 125: Returns 255

**XOR**

For positive integers x, y and for x ≥ y, the XOR function is defined as:

Σ( 2^n * [ [ floor(x/2^n) + floor(y/2^n) ] mod 2 ] from n = 0 to floor(log(x)/log(2))

**TI-84 Plus CE Program XOR**

"2020-05-11 EWS"

Disp "X XOR Y, X≥Y"

Prompt X,Y

0→T

For(N,0,X-fPart(X))

(X/2^N)-fPart(X/2^N)→A

2*fPart(A/2)→A

(Y/2^N)-fPart(Y/2^N)→B

2*fPart(B/2)→B

T+2^N*2*fPart((A+B)/2)→T

End

Disp T

Examples:

145 XOR 37: Returns 180

226 XOR 125: Returns 159

Eddie

Source:

“Bitwise Operation” Wikipedia. Page last edited May 10, 2020. Accessed on May 11, 2020.

Link: https://en.wikipedia.org/wiki/Bitwise_operation

Eddie

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